Elisha

35 Reputation

3 Badges

7 years, 58 days

MaplePrimes Activity


These are questions asked by Elisha

How can I import my data from my Ms word document to a Maple work sheet. Iam finding it difficult to save my work as a Dat file. Something like this example below

 

Data:=readdata("c:/Users/kokoge00/Desktop/methods.dat",float,10);
Data := [[0.1, 0.0769540597, 0.1477783335, 0.1393069312

  0.0763361154, 0.1477867626, 0.1393072151, 0.0763361266

  0.1477867830, 0.1393071934], [0.3, 0.1093424148, 0.1120401102

  0.1509302274, 0.1072278404, 0.1121142033, 0.1509369166

  0.1072278479, 0.1121142168, 0.1509369024], [0.5, 0.1392030568

  0.0853083077, 0.1558066181, 0.1353291378, 0.0855066806

  0.1558355785, 0.1353291558, 0.08550671332, 0.1558355439], [0.7, 

  0.1662374563, 0.0652194693, 0.1562235596, 0.1604342222

  0.0655908735, 0.1562974878, 0.1604342352, 0.06559089617, 

  0.1562974637], [0.9, 0.1903821623, 0.0500537619, 0.1537887672

  0.1825594352, 0.0506356391, 0.1539346707, 0.1825594528

  0.05063567192, 0.1539346352], [1.1, 0.2117168860, 0.0385555127

  0.1496220815, 0.2018541863, 0.0393727175, 0.1498707561

  0.2018542024, 0.03937274753, 0.1498707234], [1.3, 0.2303874000

  0.0298096396, 0.1444864012, 0.2185409755, 0.0308687065

  0.1448804021, 0.2185409880, 0.03086872986, 0.1448803765], [1.5, 

  0.2465077820, 0.0231661161, 0.1388614678, 0.2328759081

  0.0244336214, 0.1394893808, 0.2328759200, 0.02443364533, 

  0.1394893543]]
 

Please help with the bifurcation diagram for the system and parameter values below

NULL

with(VectorCalculus)

[`&x`, `*`, `+`, `-`, `.`, `<,>`, `<|>`, About, AddCoordinates, ArcLength, BasisFormat, Binormal, ConvertVector, CrossProduct, Curl, Curvature, D, Del, DirectionalDiff, Divergence, DotProduct, Flux, GetCoordinateParameters, GetCoordinates, GetNames, GetPVDescription, GetRootPoint, GetSpace, Gradient, Hessian, IsPositionVector, IsRootedVector, IsVectorField, Jacobian, Laplacian, LineInt, MapToBasis, Nabla, Norm, Normalize, PathInt, PlotPositionVector, PlotVector, PositionVector, PrincipalNormal, RadiusOfCurvature, RootedVector, ScalarPotential, SetCoordinateParameters, SetCoordinates, SpaceCurve, SurfaceInt, TNBFrame, TangentLine, TangentPlane, TangentVector, Torsion, Vector, VectorField, VectorPotential, VectorSpace, Wronskian, diff, eval, evalVF, int, limit, series]

(1)

interface(imaginaryunit = F)

I

(2)

M := Pi*theta-S*c__1-S*lambda+S__v*v__2

Pi*theta-S*c__1-S*lambda+S__v*v__2

(3)

Y := -S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

-S__v*c__2*lambda+Pi*b__1+S*v__1-S__v*c__3

(4)

P := S__v*alpha+`&rho;__A`*A+c__4*`&rho;__Q`*Q+I*`&rho;__I`-µ*V

Q*c__4*rho__Q+A*rho__A+I*rho__I+S__v*alpha-V*µ

(5)

R := S__v*c__2*lambda-E*c__5+S*lambda

S__v*c__2*lambda-E*c__5+S*lambda

(6)

U := E*a*delta+Q*k*`&rho;__Q`-A*c__6

E*a*delta+Q*k*rho__Q-A*c__6

(7)

L := c__7*E-I*c__8

E*c__7-I*c__8

(8)

X := q__E*E+I*q__I-c__9*Q

E*q__E+I*q__I-Q*c__9

(9)

solve({L = 0, M = 0, P = 0, R = 0, U = 0, X = 0, Y = 0}, {I, A, E, Q, S, S__v, V})

{A = (a*c__8*c__9*delta+c__7*k*q__I*rho__Q+c__8*k*q__E*rho__Q)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__6*c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), E = lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), I = c__7*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), Q = (c__7*q__I+c__8*q__E)*lambda*Pi*(b__1*c__1*c__2+b__1*c__2*lambda+c__2*lambda*theta+c__2*theta*v__1+b__1*v__2+c__3*theta)/(c__9*c__5*c__8*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2)), S = Pi*(c__2*lambda*theta+b__1*v__2+c__3*theta)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), S__v = Pi*(b__1*c__1+b__1*lambda+theta*v__1)/(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2), V = Pi*(a*b__1*c__1*c__2*c__8*c__9*delta*lambda*rho__A+a*b__1*c__2*c__8*c__9*delta*lambda^2*rho__A+a*c__2*c__8*c__9*delta*lambda^2*rho__A*theta+a*c__2*c__8*c__9*delta*lambda*rho__A*theta*v__1+b__1*c__1*c__2*c__4*c__6*c__7*lambda*q__I*rho__Q+b__1*c__1*c__2*c__4*c__6*c__8*lambda*q__E*rho__Q+b__1*c__1*c__2*c__7*k*lambda*q__I*rho__A*rho__Q+b__1*c__1*c__2*c__8*k*lambda*q__E*rho__A*rho__Q+b__1*c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q+b__1*c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q+b__1*c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q+b__1*c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q+c__2*c__4*c__6*c__7*lambda^2*q__I*rho__Q*theta+c__2*c__4*c__6*c__7*lambda*q__I*rho__Q*theta*v__1+c__2*c__4*c__6*c__8*lambda^2*q__E*rho__Q*theta+c__2*c__4*c__6*c__8*lambda*q__E*rho__Q*theta*v__1+c__2*c__7*k*lambda^2*q__I*rho__A*rho__Q*theta+c__2*c__7*k*lambda*q__I*rho__A*rho__Q*theta*v__1+c__2*c__8*k*lambda^2*q__E*rho__A*rho__Q*theta+c__2*c__8*k*lambda*q__E*rho__A*rho__Q*theta*v__1+a*b__1*c__8*c__9*delta*lambda*rho__A*v__2+a*c__3*c__8*c__9*delta*lambda*rho__A*theta+b__1*c__1*c__2*c__6*c__7*c__9*lambda*rho__I+b__1*c__2*c__6*c__7*c__9*lambda^2*rho__I+b__1*c__4*c__6*c__7*lambda*q__I*rho__Q*v__2+b__1*c__4*c__6*c__8*lambda*q__E*rho__Q*v__2+b__1*c__7*k*lambda*q__I*rho__A*rho__Q*v__2+b__1*c__8*k*lambda*q__E*rho__A*rho__Q*v__2+c__2*c__6*c__7*c__9*lambda^2*rho__I*theta+c__2*c__6*c__7*c__9*lambda*rho__I*theta*v__1+c__3*c__4*c__6*c__7*lambda*q__I*rho__Q*theta+c__3*c__4*c__6*c__8*lambda*q__E*rho__Q*theta+c__3*c__7*k*lambda*q__I*rho__A*rho__Q*theta+c__3*c__8*k*lambda*q__E*rho__A*rho__Q*theta+alpha*b__1*c__1*c__5*c__6*c__8*c__9+alpha*b__1*c__5*c__6*c__8*c__9*lambda+alpha*c__5*c__6*c__8*c__9*theta*v__1+b__1*c__6*c__7*c__9*lambda*rho__I*v__2+c__3*c__6*c__7*c__9*lambda*rho__I*theta)/(c__5*c__6*c__8*c__9*µ*(c__1*c__2*lambda+c__2*lambda^2+c__1*c__3+c__3*lambda-v__1*v__2))}

(10)

``

lambda := beta*(I+`&eta;__A`*A+`&eta;__Q`*Q)/N

beta*(I+eta__A*A+eta__Q*Q)/N

(11)

``

NULL

k := .15

.15

(12)

delta := .125

.125

(13)

mu := 0.464360344e-4

0.464360344e-4

(14)

pi := .464360344

.464360344

(15)

delta__Q := 0.6847e-3

0.6847e-3

(16)

beta := .1086

.1086

(17)

q__E := 0.18113e-3

0.18113e-3

(18)

rho__Q := 0.815e-1

0.815e-1

(19)

a := .16255

.16255

(20)

v__1 := 0.5e-1

0.5e-1

(21)

v__2 := 0.5e-1

0.5e-1

(22)

alpha := 0.57e-1

0.57e-1

(23)

lambda := 0.765e-2

0.765e-2

(24)

rho__A := 0.915e-1

0.915e-1

(25)

rho__I := 0.515e-1

0.515e-1

(26)

a := .16255

.16255

(27)

q__I := 0.1923e-2

0.1923e-2

(28)

q__A := 0.4013e-7

0.4013e-7

(29)

eta__A := .1213

.1213

(30)

eta__Q := 0.3808e-2

0.3808e-2

(31)

w := .5925

.5925

(32)

Download Bifurcation_Equation.mw

I find it difficult to use dsolve to solve system of ordinary differential equations with assigned parameters and initial conditions. The error message "Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names" kept coming up.

Pls see the uploaded equation for more understanding

restart

interface(imaginaryunit = F)

I

(1)

I

I

(2)

sqrt(-4)

2*I

(3)

NULL

Suscep := diff(S(t), t) = theta*epsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

diff(S(t), t) = theta*varepsilon+v__2*S__v(t)-S(t)*lambda-S(t)*(µ+v__1)

(4)

Vacc := diff(S__v(t), t) = (1-theta)*epsilon+v__1*S(t)-(µ+alpha+v__2)*S__v(t)-(1-w)*S__v(t)*lambda

Immun := diff(V(t), t) = alpha*S__v(t)+`&rho;__A`*A(t)+(1-k)*`&rho;__Q`*Q(t)+`&rho;__I`*(I)(t)-µ*V(t)

Exp := diff(E(t), t) = S(t)*lambda+(1-w)*S__v(t)*lambda-(q__E+delta+µ)*E(t)

Asymp := diff(A(t), t) = delta*a*E(t)-(`&rho;__A`+µ)*A(t)+k*`&rho;__Q`*Q(t)

Inf := diff((I)(t), t) = delta*(1-a)*E(t)-(`&rho;__I`+q__I+`&delta;__I`+µ)*(I)(t)

Quar := diff((I)(t), t) = q__E*E(t)+q__I*(I)(t)-(`&rho;__Q`+`&delta;__Q`+µ)*Q(t)

init_conds := S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, (I)(0) = I_0, Q(0) = Q_0

S(0) = S_0, S__v(0) = S__v*_0, V(0) = V_0, E(0) = E_0, A(0) = A_0, I(0) = I_0, Q(0) = Q_0

(5)

sys := {Asymp, Exp, Immun, Inf, Quar, Suscep, Vacc, init_conds}

``

sol := dsolve(sys, numeric, parameters = [`&delta;__Q`, `&delta;__I`, a, k, epsilon, v[1], q[E], q[I], q[A], eta[A], eta[Q], rho[A], rho[Q], rho[I], v[2], alpha, mu, delta, alpha, beta, w, lambda, S_0, S__v*_0, V_0, E_0, A_0, I_0, Q_0], method = rkf45)

Error, (in dsolve/numeric) 'parameters' must be specified as a list of unique unassigned names

 

sol(parameters = [delta = .125, `&delta;__Q` = 0.6847e-3, epsilon = .464360344, `&delta;__I` = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, `&rho;__Q` = 0.815e-1, `&rho;__A` = .1, `&rho;__I` = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, `&eta;__A` = .1213, `&eta;__Q` = 0.3808e-2*alpha and 0.3808e-2*alpha = .4, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

sol(parameters = [delta = .125, delta__Q = 0.6847e-3, varepsilon = .464360344, delta__I = 0.2230e-8, a = .6255, q[E] = 0.18113e-3, k = .15, v__1 = 0.5e-1, v__2 = 0.6e-1, rho__Q = 0.815e-1, rho__A = .1, rho__I = 0.666666e-1, q__I = 0.1923e-2, q__A = 0.4013e-7, eta__A = .1213, false, w = .5925, mu = 0.464360344e-4, lambda = 0.1598643e-7, S_0 = 1.0, S__v*_0 = 0.6e-4, V_0 = 0.35e-4, E_0 = 0.5e-4, I_0 = 0.32e-4, A_0 = 0.15e-4, Q_0 = 0.1e-4])

(6)

Evaluate*the*system*at*t = 2

sol(2)

sol(2)

(7)

sol(1)

sol(1)

(8)

sol(.1)

sol(.1)

(9)

sol(.3)

sol(.3)

(10)

sol(.5)

sol(.5)

(11)

sol(.7)

sol(.7)

(12)

sol(.9)

sol(.9)

(13)

sol(1.1)

sol(1.1)

(14)

sol(1.3)

sol(1.3)

(15)

sol(1.5)

sol(1.5)

(16)

 

 

Download Covid19_Simulation.mw

Dear Team, I have used RKF45 to solve my ODE with Maple. now I am required to solve same ODE using RK4 for comparison of solution. Ps help me with an example. Pls find my Parameters, intial values and ODE below:


 

``

ODE*equations

ODE*equations

(1)

diff(s(t), t) = (1-phi)*epsilon+(1-rho)*a+(1-f)*alpha*v(t)-(lambda+theta[1]+a+epsilon)*s(t)

diff(v(t), t) = phi*epsilon+rho*a+theta[1]*s(t)-((1-f)*alpha+f*theta[2]+a+epsilon)*v(t)

diff(e(t), t) = lambda*s(t)-(delta+a+epsilon)*e(t)

NULL

diff(r(t), t) = eta*i(t)+v(t)*f*theta[2]-(a+epsilon)*r(t)

``

``

My*parameters

My*parameters

(2)

v(0) := .4

.4

(3)

NULL

s(0) := 0.6e-1

0.6e-1

(4)

e[0] := .24

.24

(5)

i[0] := .17

.17

(6)

r[0] := .13

.13

(7)

c := 0.4e-1

0.4e-1

(8)

f := .4

.4

(9)

beta := .2

.2

(10)

epsilon := .8

.8

(11)

theta[1] := .1

.1

(12)

theta[2] := .3

.3

(13)

alpha := .9

.9

(14)

rho := .7

.7

(15)

eta := .99

.99

(16)

delta := .3

.3

(17)

a := 0.4e-1

0.4e-1

(18)

phi := 1

``

``

``


 

Download ODE_EQNS.mw

How can i plot various 3 multiple graphs using Maple to Compare ADM, EXACT SOLUTION AND RKF45 using the table below:

 Time  ADM Solution                                   RKF45 Numerical Solution        EXACT Solution

               ADM Solution                     RKF45 Numerical Solution                EXACT Solution

 t           s               i              r                 s            i                r             s               i                   r

0.1     0.0769540597    0.1477783335     0.1393069312      0.0763361154   0.1477867626   0.1393072151   0.0763361266    0.1477867830     0.1393071934 

0.3     0.1093424148    0.1120401102     0.1509302274      0.1072278404   0.1121142033   0.1509369166   0.1072278479    0.1121142168     0.1509369024 

0.5     0.1392030568    0.0853083077     0.1558066181      0.1353291378   0.0855066806   0.1558355785   0.1353291558    0.08550671332   0.1558355439

0.7     0.1662374563    0.0652194693     0.1562235596      0.1604342222   0.0655908735   0.1562974878   0.1604342352    0.06559089617   0.1562974637 

0.9     0.1903821623    0.0500537619     0.1537887672      0.1825594352   0.0506356391   0.1539346707   0.1825594528    0.05063567192   0.1539346352

1.1     0.2117168860    0.0385555127     0.1496220815      0.2018541863   0.0393727175   0.1498707561   0.2018542024    0.03937274753   0.1498707234 

1.3     0.2303874000    0.0298096396     0.1444864012      0.2185409755   0.0308687065   0.1448804021   0.2185409880    0.03086872986   0.1448803765 

1.5     0.2465077820    0.0231661161     0.1388614678      0.2328759081   0.0244336214   0.1394893808   0.2328759200    0.02443364533   0.1394893543

 

 

 

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