Maple 18 Questions and Posts

These are Posts and Questions associated with the product, Maple 18

how can i plot the relation betwen x and B[k] from result of itterition in this work sheetx_phi.mw

restart

with(LinearAlgebra):

lambda := 3.64*10^10

0.3640000000e11

(1)

mu := 5.46*10^10

0.5460000000e11

(2)

rho := 2330

2330

(3)

tau := 5*10^(-5)

1/20000

(4)

T[0] := 800

800

(5)

d[n] := -9*10^(-31)

-9/10000000000000000000000000000000

(6)

d[e] := 2.5*10^(-3)

0.2500000000e-2

(7)

E[g] := 1.11

1.11

(8)

C[e] := 695

695

(9)

alpha[T] := 4.14*10^(-6)

0.4140000000e-5

(10)

delta := (3*lambda+2*mu)*alpha[T];

904176.0000

(11)

r := 2

2

(12)

omega[0] := -.3

-.3

(13)

``

epsilon[0] := 8.85*10^(-12)

0.8850000000e-11

(14)

k := 800

800

(15)

C[T] := sqrt((2*mu+lambda)/rho)

7905.015521

(16)

mu[0] := (4*3.17)*10^(-7)

0.1268000000e-5

(17)

t[1] := k/(rho*C[e]*C[T]^2)

0.7905763302e-11

(18)

q[2] := k*t[1]/(d[e]*rho*tau*C[e])

0.3124518178e-7

(19)

q[1] := k/(d[e]*rho*C[e])

.1976101522

(20)

a := .5

.5

(21)

mu := 5.46*10^10

0.5460000000e11

(22)

``

q[3] := a/C[T]^2

0.8001373626e-8

(23)

epsilon[1] := delta^2*T[0]*t[1]/(k*rho)

0.2773919393e-2

(24)

epsilon[2] := alpha[T]*E[g]*t[1]/(d[n]*rho*tau*C[e])

-0.4985559321e12

(25)

kappa := 386

386

(26)

epsilon[3] := d[n]*k*kappa*t[1]/(alpha[T]*rho*C[e]*d[e])

-0.1310939149e-33

(27)

NULL

NULL

delta[n] := (3*lambda+2*mu)*d[n]

-0.1965600000e-18

(28)

H0 := 10^5

100000

(29)

R[H] := 1+epsilon[0]*((4*3.17)*10^(-7))^2*H0^2/rho

1.

(30)

alpha[0] := 1+(4*3.17)*10^(-7)*H0^2

12681.00000

(31)

nu := 2

2

(32)

for y from 0 to 300 do x := 0+0.1e-1*y; t := .8; s := 4.7/t; A[1] := -(-s^4*R[H]-s^3*R[H]*q[3]-s^3*alpha[0]*q[1]-s^2*alpha[0]*q[1]*q[3]+s^2*epsilon[2]*q[1]*q[3]-s^3*alpha[0]+s^3*epsilon[2]-s^2*alpha[0]*q[2]-s*alpha[0]*q[2]*q[3]+s*epsilon[2]*epsilon[3]*q[3]+s*epsilon[2]*q[2]*q[3]+alpha[0]*epsilon[1]*epsilon[3]*q[3])/(s^2*alpha[0]+s*alpha[0]*q[3]-s*epsilon[2]*q[3]); A[2] := (s^5*R[H]*q[1]+s^4*R[H]*q[1]*q[3]+s^5*R[H]+s^4*R[H]*q[2]+s^4*alpha[0]*q[1]-s^4*epsilon[2]*q[1]+s^3*R[H]*q[2]*q[3]-s^2*R[H]*epsilon[1]*epsilon[3]*q[3]+s^3*alpha[0]*q[2]-s^3*epsilon[2]*epsilon[3]-s^3*epsilon[2]*q[2]-s^2*alpha[0]*epsilon[1]*epsilon[3])/(s^2*alpha[0]+s*alpha[0]*q[3]-s*epsilon[2]*q[3]); A[3] := (-s^6*R[H]*q[1]-s^5*R[H]*q[2]+s^4*R[H]*epsilon[1]*epsilon[3])/(-s^2*alpha[0]-s*alpha[0]*q[3]+s*epsilon[2]*q[3]); M[1] := (1/6)*sqrt(6)*sqrt((8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*((8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)+2*A[1]*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)+4*A[1]^2-12*A[2]))/(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); M[2] := (1/6)*sqrt(3)*sqrt((8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*(I*sqrt(3)*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-(4*I)*sqrt(3)*A[1]^2+(12*I)*sqrt(3)*A[2]-(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)+4*A[1]*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)-4*A[1]^2+12*A[2]))/(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); M[3] := (1/6)*sqrt(-3*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)*(I*sqrt(3)*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-(4*I)*sqrt(3)*A[1]^2+(12*I)*sqrt(3)*A[2]+(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(2/3)-4*A[1]*(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3)+4*A[1]^2-12*A[2]))/(8*A[1]^3-36*A[2]*A[1]+108*A[3]+12*sqrt(12*A[1]^3*A[3]-3*A[1]^2*A[2]^2-54*A[1]*A[2]*A[3]+12*A[2]^3+81*A[3]^2))^(1/3); m[1, 1] := -(M[1]^2*q[3]-s^2)/s^2; m[1, 2] := -(M[2]^2*q[3]-s^2)/s^2; m[1, 3] := -(M[3]^2*q[3]-s^2)/s^2; m[2, 1] := epsilon[3]*(M[1]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[1]^2-q[2])); m[2, 2] := epsilon[3]*(M[2]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[2]^2-q[2])); m[2, 3] := epsilon[3]*(M[3]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[3]^2-q[2])); m[3, 1] := (-M[1]*(M[1]^2*q[3]-s^2)*(-s*q[1]+M[1]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[1]^2-q[2])*(-s^2*R[H]+M[1]^2*alpha[0]))-epsilon[3]*(M[1]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[1]^2-q[2]))+(M[1]^2*q[3]-s^2)/s^2)/mu; m[3, 2] := (-M[2]*(M[2]^2*q[3]-s^2)*(-s*q[1]+M[2]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[2]^2-q[2])*(-s^2*R[H]+M[2]^2*alpha[0]))-epsilon[3]*(M[2]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[2]^2-q[2]))+(M[2]^2*q[3]-s^2)/s^2)/mu; m[3, 3] := (-M[3]*(M[3]^2*q[3]-s^2)*(-s*q[1]+M[3]^2-epsilon[3]-q[2])/(s^2*(-s*q[1]+M[3]^2-q[2])*(-s^2*R[H]+M[3]^2*alpha[0]))-epsilon[3]*(M[3]^2*q[3]-s^2)/(s^2*(-s*q[1]+M[3]^2-q[2]))+(M[3]^2*q[3]-s^2)/s^2)/mu; V[1] := (m[2, 2]*m[3, 3]-m[2, 3]*m[3, 2])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)-(m[1, 2]*m[3, 3]-m[1, 3]*m[3, 2])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); V[2] := -(m[2, 1]*m[3, 3]-m[2, 3]*m[3, 1])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)+(m[1, 1]*m[3, 3]-m[1, 3]*m[3, 1])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); V[3] := (m[2, 1]*m[3, 2]-m[2, 2]*m[3, 1])*T[0]/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r)-(m[1, 1]*m[3, 2]-m[1, 2]*m[3, 1])*nu/((m[1, 1]*m[2, 2]*m[3, 3]-m[1, 1]*m[2, 3]*m[3, 2]-m[1, 2]*m[2, 1]*m[3, 3]+m[1, 2]*m[2, 3]*m[3, 1]+m[1, 3]*m[2, 1]*m[3, 2]-m[1, 3]*m[2, 2]*m[3, 1])*r*d[e]); F[k] := sum(exp(-M[i]*x)*V[i], i = 1 .. 3); s := (4.7+I*m*Pi)/(.8); G[k] := sum((sum(exp(-M[i]*x)*V[i], i = 1 .. 3))(-1)^(4.7/t), m = 1 .. 1000); B[k] := exp(4.7)*Re((1/2)*F[k]+G[k])/t; print(x, B[k]/10^213) end do:

0., 0.1992794392e-4

 

0.1e-1, 405.1968646

 

0.2e-1, 390.9497022

 

0.3e-1, 376.7508308

 

0.4e-1, 362.6447807

 

0.5e-1, 348.6712262

 

0.6e-1, 334.8653546

 

0.7e-1, 321.2582106

 

0.8e-1, 307.8770196

 

0.9e-1, 294.7454880

 

.10, 281.8840866

 

.11, 269.3103112

 

.12, 257.0389286

 

.13, 245.0822062

 

.14, 233.4501244

 

.15, 222.1505743

 

.16, 211.1895453

 

.17, 200.5712947

 

.18, 190.2985093

 

.19, 177.1851378

 

.20, 163.5721140

 

.21, 150.7945764

 

.22, 138.8106908

 

.23, 127.5802985

 

.24, 117.0648679

 

.25, 107.2274480

 

.26, 98.03262160

 

.27, 89.44645840

 

.28, 81.43646938

 

.29, 73.97156169

 

.30, 67.02199266

 

.31, 60.55932687

 

.32, 54.55639165

 

.33, 48.98723509

 

.34, 43.82708326

 

.35, 39.05229999

 

.36, 34.64034546

 

.37, 30.56973756

 

.38, 26.82001293

 

.39, 23.37168921

 

.40, 20.20622852

 

.41, 17.30600112

 

.42, 14.65425098

 

.43, 12.23506127

 

.44, 10.03332140

 

.45, 8.034694822

 

.46, 6.225587898

 

.47, 4.593118969

 

.48, 3.125089577

 

.49, 1.809955352

 

.50, .6367985224

 

.51, -.4046990616

 

.52, -1.324281757

 

.53, -2.131145339

 

.54, -2.833961366

 

.55, -3.440900557

 

.56, -3.959655544

 

.57, -4.397462807

 

.58, -4.761123780

 

.59, -5.057025096

 

.60, -5.291158522

 

.61, -5.469139620

 

.62, -5.596226100

 

.63, -5.677335363

 

.64, -5.717061286

 

.65, -5.719690555

 

.66, -5.689218249

 

.67, -5.629362675

 

.68, -5.543579981

 

.69, -5.435077780

 

.70, -5.306828427

 

.71, -5.161581784

 

.72, -5.001877308

 

.73, -4.830055721

 

.74, -4.648270190

 

.75, -4.458496938

 

.76, -4.262545543

 

.77, -4.062068598

 

.78, -3.858571095

 

.79, -3.653419299

 

.80, -3.447849233

 

.81, -3.242974818

 

.82, -3.039795550

 

.83, -2.839203889

 

.84, -2.641992256

 

.85, -2.448859703

 

.86, -2.260418251

 

.87, -2.077198928

 

.88, -1.899657470

 

.89, -1.728179795

 

.90, -1.563087142

 

.91, -1.404640926

 

.92, -1.253047446

 

.93, -1.108462174

 

.94, -.9709939859

 

.95, -.8407090153

 

.96, -.7176343927

 

.97, -.6017617225

 

.98, -.4930503695

 

.99, -.3914305768

 

1.00, -.2968063580

 

1.01, -.2090582474

 

1.02, -.1280458807

 

1.03, -0.5361039903e-1

 

1.04, 0.1442329617e-1

 

1.05, 0.7624440011e-1

 

1.06, .1320542742

 

1.07, .1820645715

 

1.08, .2264955283

 

1.09, .2655743625

 

1.10, .2995338094

 

1.11, .3286107310

 

1.12, .3530448641

 

1.13, .3730776218

 

1.14, .3889510461

 

1.15, .4009068006

 

1.16, .4091852736

 

1.17, .4140247375

 

1.18, .4156606158

 

1.19, .4143247938

 

1.20, .4102450006

 

1.21, .4036442692

 

1.22, .3947404353

 

1.23, .3837457124

 

1.24, .3708663038

 

1.25, .3563020723

 

1.26, .3402462557

 

1.27, .3228852236

 

1.28, .3043982786

 

1.29, .2849574921

 

1.30, .2647275751

 

1.31, .2438657908

 

1.32, .2225218850

 

1.33, .2008380578

 

1.34, .1789489531

 

1.35, .1569816739

 

1.36, .1350558249

 

1.37, .1132835796

 

1.38, 0.9176974401e-1

 

1.39, 0.7061187116e-1

 

1.40, 0.4990036538e-1

 

1.41, 0.2971860988e-1

 

1.42, 0.1014311718e-1

 

1.43, -0.8756330759e-2

 

1.44, -0.2691651136e-1

 

1.45, -0.4428059057e-1

 

1.46, -0.6079793867e-1

 

1.47, -0.7642394939e-1

 

1.48, -0.9111983792e-1

 

1.49, -.1048524503

 

1.50, -.1175940457

 

1.51, -.1293221053

 

1.52, -.1400191110

 

1.53, -.1496723398

 

1.54, -.1582736461

 

1.55, -.1658192483

 

1.56, -.1723095185

 

1.57, -.1777487660

 

1.58, -.1821450266

 

1.59, -.1855098472

 

1.60, -.1878580843

 

1.61, -.1892076902

 

1.62, -.1895795127

 

1.63, -.1889970940

 

1.64, -.1874864724

 

1.65, -.1850759882

 

1.66, -.1817960960

 

1.67, -.1776791744

 

1.68, -.1727593506

 

1.69, -.1670723178

 

1.70, -.1606551675

 

1.71, -.1535462209

 

1.72, -.1457848648

 

1.73, -.1374113982

 

1.74, -.1284668778

 

1.75, -.1189929708

 

1.76, -.1090318171

 

1.77, -0.9862588936e-1

 

1.78, -0.8781786615e-1

 

1.79, -0.7665050397e-1

 

1.80, -0.6516651986e-1

 

1.81, -0.5340847477e-1

 

1.82, -0.4141866772e-1

 

1.83, -0.2923903059e-1

 

1.84, -0.1691103000e-1

 

1.85, -0.4475574873e-2

 

1.86, 0.8027071258e-2

 

1.87, 0.2055737256e-1

 

1.88, 0.3307659754e-1

 

1.89, 0.4554689214e-1

 

1.90, 0.5793134849e-1

 

1.91, 0.7019406310e-1

 

1.92, 0.8230019855e-1

 

1.93, 0.9421603540e-1

 

1.94, .1059090207

 

1.95, .1173478117

 

1.96, .1285023130

 

1.97, .1393437184

 

1.98, .1498445350

 

1.99, .1599786176

 

2.00, .1697211843

 

2.01, .1790488398

 

2.02, .1879395952

 

2.03, .1963728739

 

2.04, .2043295246

 

2.05, .2117918242

 

2.06, .2187434816

 

2.07, .2251696396

 

2.08, .2310568678

 

2.09, .2363931559

 

2.10, .2411679087

 

2.11, .2453719318

 

2.12, .2489974201

 

2.13, .2520379316

 

2.14, .2544883873

 

2.15, .2563450336

 

2.16, .2576054280

 

2.17, .2582684148

 

2.18, .2583340904

 

2.19, .2578037910

 

2.20, .2566800472

 

2.21, .2549665668

 

2.22, .2526681898

 

2.23, .2497908663

 

2.24, .2463416160

 

2.25, .2423284949

 

2.26, .2377605558

 

2.27, .2326478187

 

2.28, .2270012215

 

2.29, .2208325951

 

2.30, .2141546081

 

2.31, .2069807476

 

2.32, .1993252583

 

2.33, .1912031162

 

2.34, .1826299809

 

2.35, .1736221655

 

2.36, .1641965755

 

2.37, .1543706937

 

2.38, .1441625153

 

2.39, .1335905282

 

2.40, .1226736599

 

2.41, .1114312327

 

2.42, 0.9988294660e-1

 

2.43, 0.8804880801e-1

 

2.44, 0.7594912341e-1

 

2.45, 0.6360442901e-1

 

2.46, 0.5103548172e-1

 

2.47, 0.3826319666e-1

 

2.48, 0.2530863187e-1

 

2.49, 0.1219293308e-1

 

2.50, -0.1062687499e-2

 

2.51, -0.1443699931e-1

 

2.52, -0.2790877250e-1

 

2.53, -0.4145683033e-1

 

2.54, -0.5506005799e-1

 

2.55, -0.6869746087e-1

 

2.56, -0.8234817347e-1

 

2.57, -0.9599150501e-1

 

2.58, -.1096069557

 

2.59, -.1231742615

 

2.60, -.1366734005

 

2.61, -.1500846438

 

2.62, -.1633885522

 

2.63, -.1765660349

 

2.64, -.1895983404

 

2.65, -.2024670969

 

2.66, -.2151543339

 

2.67, -.2276425010

 

2.68, -.2399144754

 

2.69, -.2519536023

 

2.70, -.2637436967

 

2.71, -.2752690610

 

2.72, -.2865145057

 

2.73, -.2974653604

 

2.74, -.3081074905

 

2.75, -.3184273102

 

2.76, -.3284117843

 

2.77, -.3380484505

 

2.78, -.3473254268

 

2.79, -.3562314068

 

2.80, -.3647556901

 

2.81, -.3728881654

 

2.82, -.3806193364

 

2.83, -.3879403119

 

2.84, -.3948428203

 

2.85, -.4013191999

 

2.86, -.4073624159

 

2.87, -.4129660473

 

2.88, -.4181242979

 

2.89, -.4228319938

 

2.90, -.4270845748

 

2.91, -.4308781034

 

2.92, -.4342092550

 

2.93, -.4370753080

 

2.94, -.4394741607

 

2.95, -.4414043009

 

2.96, -.4428648179

 

2.97, -.4438553898

 

2.98, -.4443762751

 

2.99, -.4444283083

 

3.00, -.4440128867

(33)

;

``


 

Download x_phi.mw

 

I'm getting no solution for the attached pdf.  Kindly suggest!

Maple Worksheet - Error

pde.mw


 

restart; with(plots); with(Optimization); with(Statistics)

A := 0.346e-1; mu := 0.491e-1
Parameterizing (with respect to l, m, n, rho, k, q, r, u, v, sigma, iota, nu, phi, upsilon, w, x, delta, g) the numerical solution of the model deq
      #Calculating the sum of the square of the errors between the model predictions and experimental data
     #Minimizing the sum of the square of the errors to find the best fit values of " l, m, n ,rho, k, q, r, u , v , sigma, iota, nu, phi,upsilon, w, x, delta, g."

0.346e-1

 

0.491e-1

(1)

times := [5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100];

[5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100]

(2)

C__f := [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 8, 12, 12, 22, 30, 40, 44, 51, 65, 70, 97, 111, 131, 135, 174, 184, 210, 214, 232, 238, 254, 276, 285, 305, 318, 323, 343, 373, 407, 442, 493, 542, 627, 665, 782, 873, 981, 1095, 1182, 1273, 1337, 1532, 1728, 1932, 2170, 2388, 2558, 2802, 2950, 3145, 3526, 3912, 4151, 4399, 4641, 4787, 4971, 5162, 5445, 5621, 5959, 6175, 6401, 6677, 7016, 7261, 7526, 7839, 8068, 8344, 8733, 8915, 9302, 9855, 10162, 10819, 11166, 11516, 11844, 12233, 12486, 12801, 13464, 13873, 14554, 15181, 15682, 16085, 16658, 17148, 17735]

DE1 := diff(B(T), T) = A-l*B(T)*C(T)/(1+sigma*C(T))-nu*m*B(T)*P(T)/(1+iota*P(T))-mu*B(T)-n*B(T)*E(T)/(E(T)+g):

res := dsolve({DE1, DE2, DE3, DE4, DE5}, parameters = [l, m, n, rho, k, q, r, u, v, sigma, iota, nu, phi, upsilon, w, x, delta, g], numeric)

Error, (in dsolve/numeric/type_check) insufficient initial/boundary value information for procedure defined problem

 

Typesetting:-mrow(Typesetting:-mi("sse", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo("proc", bold = "true", mathvariant = "bold", fontweight = "bold", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("l", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("m", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("n", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("rho", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("k", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("q", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("r", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("u", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("v", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("sigma", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("iota", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nu", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("phi", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("upsilon", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("w", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("delta", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("res", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("parameters", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("l", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("m", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("n", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("rho", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("k", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("q", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("r", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("u", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("v", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("sigma", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("iota", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nu", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("phi", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("upsilon", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("w", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("delta", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi(""), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msup(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-msub(Typesetting:-mi("C", italic = "true", mathvariant = "italic"), Typesetting:-mrow(Typesetting:-mi("f", italic = "true", mathvariant = "italic")), subscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("i", italic = "true", mathvariant = "italic")), mathvariant = "normal", open = "[", close = "]"), Typesetting:-mo("−", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2222222em", rspace = "0.2222222em"), Typesetting:-mi("rhs", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("select", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("has", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("res", italic = "true", mathvariant = 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"false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("Minimize the sum of the square of errors ", italic = "true", mathvariant = "italic"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("optPars", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("Minimize", italic = "true", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("'", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.0em"), Typesetting:-mi("sse", italic = "true", mathvariant = "italic"), Typesetting:-mo("'", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.1111111em", rspace = "0.0em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("l", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("m", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("n", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("rho", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("k", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("q", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("r", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("u", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("v", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("sigma", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("iota", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nu", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("phi", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("upsilon", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("w", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("delta", italic = "false", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g", italic = "true", mathvariant = "italic")), mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("initialpoint", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("l", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.05", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("m", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.02", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("n", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0.017", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("rho", italic = "false", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.7", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("k", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.091", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("q", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.004", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("r", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.098710", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("u", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0100", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("v", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.08543", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("sigma", italic = "false", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0.0349", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("iota", italic = "false", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0032", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("nu", italic = "false", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0014", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("phi", italic = "false", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.931", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("upsilon", italic = "false", mathvariant = "normal"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.0019", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("w", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.00398", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("x", italic = "true", mathvariant = "italic"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.00901", mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("delta", italic = "false", mathvariant = "normal"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.01", mathvariant = "normal"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mi("g", italic = "true", mathvariant = "italic"), Typesetting:-mo("≔", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mn("0.3", mathvariant = "normal")), mathvariant = "normal", open = "{", close = "}"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("assume", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mi("nonnegative", italic = "true", mathvariant = "italic"), Typesetting:-mo(",", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.3333333em"), Typesetting:-mi("optimalitytolerance", italic = "true", mathvariant = "italic"), Typesetting:-mo("=", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.2777778em", rspace = "0.2777778em"), Typesetting:-mn("0.00001", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(";", mathvariant = "normal", fence = "false", separator = "true", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.2777778em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"), Typesetting:-mspace(height = "0.0ex", width = "0.0em", depth = "0.0ex", linebreak = "newline"), Typesetting:-mo(" ", mathvariant = "normal", fence = "false", separator = "false", stretchy = "false", symmetric = "false", largeop = "false", movablelimits = "false", accent = "false", lspace = "0.0em", rspace = "0.0em"))

``


 

 

Dear maple users @acer @Carl Love @Kitonum @Preben Alsholm @dharr @tomleslie

Greeting.

I have solved some PDEs in analytically and numerically.

But the numerical and analytical results are not matching.

I hope there is some problem with an analytical solution, especially in the first order and second-order boundary conditions.

Both the codes have enclosed here, waiting for a reply.

AN.mw

NUM.mw

Note: The PDEs are performed in the Maple 18 version. 

When compiling an analytical solution, in clarify expression click the remember table assignment.

 

Dear colleagues,

 

how can i plot streamlines and isothermes and also 3D graphes of Nussult number and skin friction coefficient for boundary layer flow problem with Maple? 

Regards

Berham.

MagBVP.mw

MagBVP.docx

Trying to get a curve of two data points but the graph is not a curve.

with(Statistics):

``

l1 := plot(X, t = 0 .. 16, thickness = 4, linestyle = dash, color = red):

 

``

Download fitting.mw

## i need to get a curve, but the graph is not displaying a curve fit

 

Dear maple users,

Greetings.

Q1.How to plot a figure for different values of M?

      like M=1,2,3,4:

Code:Mplot.mw

Q2. How to assign all the expressions are "remember table assignment"

Dear Maple Users @acer @Carl Love @Kitonum @Preben Alsholm ,

Greetings.

How to plot a function "Am" for various values of "kt"(eg: kt=-1..1) at a point x=0.

Am vs kt.

The code has provided below.

Waiting for your response.

ktplot.mw

 

Hallo;
the following MAPLE code generates 2-vectors. To collect them into a set K unfortunately does not work. K contains vectors two-fold etc. So K is not a set which I hoped to get. What is wrong?

restart:m:=5;#m Module
with(LinearAlgebra[Modular]):
K:={};
M:=Matrix([[3, 4*168], [4,3]]);
L:=Matrix([[3],[4]]);
#with(LinearAlgebra[Modular]):
for s from 0 to 10 do
a:=Mod(m,(M^s).L,integer);
K:=K union {a};
od:
K:=K;

Gerd

Dear maple users,

Greetings.

How to plot a contour for the below-mentioned function.

f(x):=-0.09465519086 x^3+0.02711194463 x^2+0.3862193003 x-0.00030060626-0.0003613678673 x^6-0.001538973646 x^5-0.01937304057 x^4-3.822344860 10^(-8) x^8-0.000007297718101 x^7

 

How can I generate a code to plot the optimals; h, chi and psi?


 

restart;

with(PDEtools):

with(plot):

Error, invalid input: with expects its 1st argument, pname, to be of type {`module`, package}, but received plot

 

A1:=Matrix([[phi,(chi),conjugate(phi),conjugate(chi)],
          [chi,(phi),conjugate(chi),conjugate(phi)],
          [lambda*phi,-(lambda)*(chi),
           conjugate(lambda)*conjugate(phi),-conjugate(lambda)*conjugate(chi)],
          [lambda*chi,-(lambda)*(phi),
           conjugate(lambda)*conjugate(chi),-conjugate(lambda)*conjugate(phi)]]);

A1 := Matrix(4, 4, {(1, 1) = phi, (1, 2) = chi, (1, 3) = conjugate(phi), (1, 4) = conjugate(chi), (2, 1) = chi, (2, 2) = phi, (2, 3) = conjugate(chi), (2, 4) = conjugate(phi), (3, 1) = lambda*phi, (3, 2) = -lambda*chi, (3, 3) = conjugate(lambda)*conjugate(phi), (3, 4) = -conjugate(lambda)*conjugate(chi), (4, 1) = lambda*chi, (4, 2) = -lambda*phi, (4, 3) = conjugate(lambda)*conjugate(chi), (4, 4) = -conjugate(lambda)*conjugate(phi)})

(1)

d1 := LinearAlgebra:-Determinant(A1):

d1; length(%);

conjugate(lambda)^2*conjugate(phi)^2*chi^2-conjugate(lambda)^2*conjugate(phi)^2*phi^2-conjugate(lambda)^2*conjugate(chi)^2*chi^2+conjugate(lambda)^2*conjugate(chi)^2*phi^2+2*conjugate(lambda)*conjugate(phi)^2*chi^2*lambda+2*conjugate(lambda)*conjugate(phi)^2*lambda*phi^2-8*conjugate(lambda)*conjugate(phi)*conjugate(chi)*chi*lambda*phi+2*conjugate(lambda)*conjugate(chi)^2*chi^2*lambda+2*conjugate(lambda)*conjugate(chi)^2*lambda*phi^2+conjugate(phi)^2*chi^2*lambda^2-conjugate(phi)^2*lambda^2*phi^2-conjugate(chi)^2*chi^2*lambda^2+conjugate(chi)^2*lambda^2*phi^2

 

705

(2)

den:=simplify(d1,size); length(%);

-(-(conjugate(chi)-conjugate(phi))*(chi+phi)*conjugate(lambda)+lambda*(conjugate(chi)+conjugate(phi))*(chi-phi))*(-(conjugate(chi)+conjugate(phi))*(chi-phi)*conjugate(lambda)+lambda*(conjugate(chi)-conjugate(phi))*(chi+phi))

 

333

(3)

 

con1:=phi=exp(I*lambda*(x-t/(4*lambda^2)-w^2)):con2:=chi=exp(-I*lambda*(x-t/(4*lambda^2)-w^2)):

 

den1:=simplify(dsubs({con1,con2},den));

4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*conjugate(lambda)*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda+8*conjugate(lambda)*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda^2-4*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda^2-16*conjugate(lambda)*lambda

(4)

plot3d(subs(Re(lambda)=1, Im(lambda)=.2, w=1, rhs(den1)),x=-6..6, t=-6..6)

Warning, inserted missing semicolon at end of statement

 

Error, invalid input: rhs received 4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*conjugate(lambda)*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda+8*conjugate(lambda)*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*...

 

NULL

``

 

``


 

Download 23May(1).mw


 

``

lambda := .3:

omega := lambda+mu+xi:

alpha := 2*sqrt(lambda*mu)

.9165151390

(1)

``

B[1] := BesselI(k-1, alpha*(u-y))

BesselI(k-1, .9165151390-.9165151390*y)

(2)

B[2] := BesselI(k+1, alpha*(u-y))

BesselI(k+1, .9165151390-.9165151390*y)

(3)

``

F := evalf(Int(sum((B[1]-B[2])*exp(-omega*(u-y)), k = 1 .. infinity), y = 0 .. u))

Int(sum((BesselI(k-1., .9165151390-.9165151390*y)-1.*BesselI(k+1., .9165151390-.9165151390*y))*exp(-1.200000000+1.200000000*y), k = 1 .. infinity), y = 0. .. 1.)

(4)

``

``

``


 

Download int.mw

> den := -(-(conjugate(chi)-conjugate(phi))*(chi+phi)*conjugate(lambda)+lambda*(conjugate(chi)+conjugate(phi))*(chi-phi))*(-(conjugate(chi)+conjugate(phi))*(chi-phi)*conjugate(lambda)+lambda*(conjugate(chi)-conjugate(phi))*(chi+phi));

> phi:=exp(I*lambda*(x-t/(4*lambda^2)-w^2)):chi:=exp(-I*lambda*(x-t/(4*lambda^2)-w^2)):

> den1:=simplify(dsubs({phi,chi},den));

> dsubs({exp((1/4*I)*(4*lambda^2*w^2-4*lambda^2*x+t)/lambda), exp(-(1/4*I)*(4*lambda^2*w^2-4*lambda^2*x+t)/lambda)}, 4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*abs(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2+8*abs(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda^2-4*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda^2-16*abs(lambda)^2)