Maple 2018 Questions and Posts

These are Posts and Questions associated with the product, Maple 2018

I'm using NLPSolve to minimize a complicated function. It works great, but the answers are not returned in numerical form which I need as they are then input for the next stage of my program.

How to I extract numbers?

S2 := NLPSolve(test, phi1 = 0 .. 2*Pi, phi2 = 1.0*Pi .. 2*Pi);
     S2 := [-1.00000000011810774, 

       [phi1 = 0.773215730257661, phi2 = 5.98741001513872]]
==>The Result is a list and the solutions appear kind of string-like. 

S2[2,1] returns 'phi=0.773...' not the number I need

restart:

  ra:=2: b1:=1.41: na:=0.7: we:=0.5: eta[1]:=4*0.1: d:=0.5:
  xi:=0.1: m:=na: ea:=0.5: pr:=21: gr:=0.1: R:=0.9323556933:

  PDE1:=ra*(diff(f(x,t),t))=+b1*(1+ea*cos(t))+(1/(R^2))*((diff(f(x,t),x,x))+(1/x)*diff(f(x,t),x));
  IBC:= {D[1](f)(0,t)=0,f(1,t)=0,f(x,0)=0};

2*(diff(f(x, t), t)) = 1.41+.705*cos(t)+1.150367877*(diff(diff(f(x, t), x), x))+1.150367877*(diff(f(x, t), x))/x

 

{f(1, t) = 0, f(x, 0) = 0, (D[1](f))(0, t) = 0}

(1)

sol := pdsolve({PDE1}, IBC, numeric); sol:-plot(f(x, t), t = 1.2, linestyle = "solid", title = "Velocity Profile", labels = ["r", "f"])

 

``

Download pde.mw

for different time plot of f(x,t) in single plot with different color 

modifed_practice.mw

Impact of Shape-Dependent Hybrid Nanofluid on Transient Efficiency of a Fully W
et Porous Longitudinal Fin

dear sir please help me to solve the graph i given reference pdf also. i have implimented the code but getting error in ploting 

Thank you

restart;
alias(u = u(x, y, t), f = f(x, y, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*t);
                    /     (1/2)\           
                    \f + R     / exp(I R t)
pde1 := I*(diff(u, t))+diff(u, x, x)+2*lambda*u*abs(u)*abs(u)-gamma*(diff(u, x, t));
   // d   \                /     (1/2)\             \
 I ||--- f| exp(I R t) + I \f + R     / R exp(I R t)|
   \\ dt  /                                         /

      / d  / d   \\           
    + |--- |--- f|| exp(I R t)
      \ dx \ dx  //           

               /     (1/2)\                           2 
    + 2 lambda \f + R     / exp(I R t) (exp(-Im(R t)))  

               2
   |     (1/2)| 
   |f + R     | 

            // d  / d   \\                / d   \             \
    - gamma ||--- |--- f|| exp(I R t) + I |--- f| R exp(I R t)|
            \\ dx \ dt  //                \ dx  /             /
 

      

how to plot graphs for both methods and comparison of different method values for Diff(f(eta),eta, eta) at eta =0

 

NULL

NULL

restart

F[0] := al

F[1] := a2

F[2] := a3

F[3] := a4

G[0] := a5

G[1] := a6

T[0] := a7

T[1] := a8

Q[0] := a9

Q[1] := a10

n[1] := 1

for k from 0 to n[1] do F[k+4] := solve((1+a)*(k+1)*(k+2)*(k+3)*(k+4)*F[k+4]-a*(k+1)*(k+2)*G[k+2]-R*(sum(F[k-m]*(m+1)*(m+2)*(m+3)*F[m+3], m = 0 .. k))+R*(sum((k-m+1)*F[k-m+1]*(m+1)*(m+2)*F[m+2], m = 0 .. k)), F[k+4]) end do

-(1/12)*(R*a2*a3-3*R*a4*al-a*G[2])/(1+a)

 

-(1/60)*(R^2*a2*a3*al-3*R^2*a4*al^2+2*R*a*a3^2-R*a*al*G[2]+2*R*a3^2-3*a^2*G[3]-3*a*G[3])/(1+a)^2

(1)

n[2] := 3

for k from 0 to n[2] do G[k+2] := solve(b*(k+1)*(k+2)*G[k+2]+a*(k+1)*(k+2)*F[k+2]-2*a*G[k]-c*R*(sum((m+1)*G[m+1]*F[k-m], m = 0 .. k))+c*R*(sum(G[k-m]*(m+1)*F[m+1], m = 0 .. k)), G[k+2]) end do

-(1/2)*(R*a2*a5*c-R*a6*al*c+2*a*a3-2*a*a5)/b

 

-(1/6)*(R^2*a2*a5*al*c^2-R^2*a6*al^2*c^2+2*R*a*a3*al*c-2*R*a*a5*al*c+2*R*a3*a5*b*c+6*a*a4*b-2*a*a6*b)/b^2

 

-(1/24)*(R^3*a*a2*a5*al^2*c^3-R^3*a*a6*al^3*c^3+R^3*a2*a5*al^2*c^3-R^3*a6*al^3*c^3+2*R^2*a^2*a3*al^2*c^2-2*R^2*a^2*a5*al^2*c^2+R^2*a*a2^2*a5*b*c^2-R^2*a*a2*a6*al*b*c^2+2*R^2*a*a3*a5*al*b*c^2+2*R^2*a*a3*al^2*c^2-2*R^2*a*a5*al^2*c^2+R^2*a2^2*a5*b*c^2-R^2*a2*a6*al*b*c^2+2*R^2*a3*a5*al*b*c^2+2*R*a^2*a2*a3*b*c-R*a^2*a2*a5*b*c+6*R*a^2*a4*al*b*c-3*R*a^2*a6*al*b*c+2*R*a*a3*a6*b^2*c+6*R*a*a4*a5*b^2*c-2*R*a*a2*a3*b^2+2*R*a*a2*a3*b*c+6*R*a*a4*al*b^2+6*R*a*a4*al*b*c-4*R*a*a6*al*b*c+2*R*a3*a6*b^2*c+6*R*a4*a5*b^2*c+2*a^3*a3*b-2*a^3*a5*b+4*a^2*a3*b-4*a^2*a5*b)/(b^3*(1+a))

 

-(1/120)*(R^4*a^2*a2*a5*al^3*c^4-R^4*a^2*a6*al^4*c^4+2*R^4*a*a2*a5*al^3*c^4-2*R^4*a*a6*al^4*c^4+R^4*a2*a5*al^3*c^4-R^4*a6*al^4*c^4+2*R^3*a^3*a3*al^3*c^3-2*R^3*a^3*a5*al^3*c^3+3*R^3*a^2*a2^2*a5*al*b*c^3-3*R^3*a^2*a2*a6*al^2*b*c^3+2*R^3*a^2*a3*a5*al^2*b*c^3+4*R^3*a^2*a3*al^3*c^3-4*R^3*a^2*a5*al^3*c^3+6*R^3*a*a2^2*a5*al*b*c^3-6*R^3*a*a2*a6*al^2*b*c^3+4*R^3*a*a3*a5*al^2*b*c^3+2*R^3*a*a3*al^3*c^3-2*R^3*a*a5*al^3*c^3+3*R^3*a2^2*a5*al*b*c^3-3*R^3*a2*a6*al^2*b*c^3+2*R^3*a3*a5*al^2*b*c^3+6*R^2*a^3*a2*a3*al*b*c^2-4*R^2*a^3*a2*a5*al*b*c^2+6*R^2*a^3*a4*al^2*b*c^2-4*R^2*a^3*a6*al^2*b*c^2+4*R^2*a^2*a2*a3*a5*b^2*c^2-R^2*a^2*a2*a5^2*b^2*c^2+2*R^2*a^2*a3*a6*al*b^2*c^2+6*R^2*a^2*a4*a5*al*b^2*c^2+R^2*a^2*a5*a6*al*b^2*c^2-2*R^2*a^2*a2*a3*al*b^2*c+12*R^2*a^2*a2*a3*al*b*c^2-R^2*a^2*a2*a5*al*b^2*c-6*R^2*a^2*a2*a5*al*b*c^2+6*R^2*a^2*a4*al^2*b^2*c+12*R^2*a^2*a4*al^2*b*c^2+R^2*a^2*a6*al^2*b^2*c-10*R^2*a^2*a6*al^2*b*c^2-2*R^2*a*a2*a3*a5*b^3*c+8*R^2*a*a2*a3*a5*b^2*c^2-R^2*a*a2*a5^2*b^2*c^2+4*R^2*a*a3*a6*al*b^2*c^2+6*R^2*a*a4*a5*al*b^3*c+12*R^2*a*a4*a5*al*b^2*c^2+R^2*a*a5*a6*al*b^2*c^2-2*R^2*a*a2*a3*al*b^3-2*R^2*a*a2*a3*al*b^2*c+6*R^2*a*a2*a3*al*b*c^2-2*R^2*a*a2*a5*al*b*c^2+6*R^2*a*a4*al^2*b^3+6*R^2*a*a4*al^2*b^2*c+6*R^2*a*a4*al^2*b*c^2-6*R^2*a*a6*al^2*b*c^2-2*R^2*a2*a3*a5*b^3*c+4*R^2*a2*a3*a5*b^2*c^2+2*R^2*a3*a6*al*b^2*c^2+6*R^2*a4*a5*al*b^3*c+6*R^2*a4*a5*al*b^2*c^2+4*R*a^4*a3*al*b*c-4*R*a^4*a5*al*b*c+12*R*a^3*a2*a4*b^2*c-4*R*a^3*a2*a6*b^2*c+2*R*a^3*a5^2*b^2*c+12*R*a^2*a4*a6*b^3*c-2*R*a^3*a3*al*b^2+12*R*a^3*a3*al*b*c+2*R*a^3*a5*al*b^2-12*R*a^3*a5*al*b*c+24*R*a^2*a2*a4*b^2*c-8*R*a^2*a2*a6*b^2*c-4*R*a^2*a3^2*b^3+4*R*a^2*a3*a5*b^2*c+2*R*a^2*a5^2*b^2*c+24*R*a*a4*a6*b^3*c+8*R*a^2*a3*al*b*c-8*R*a^2*a5*al*b*c+12*R*a*a2*a4*b^2*c-4*R*a*a2*a6*b^2*c-4*R*a*a3^2*b^3+4*R*a*a3*a5*b^2*c+12*R*a4*a6*b^3*c+6*a^4*a4*b^2-2*a^4*a6*b^2+18*a^3*a4*b^2-6*a^3*a6*b^2+12*a^2*a4*b^2-4*a^2*a6*b^2)/(b^4*(1+a)^2)

(2)

n[3] := 3

for k from 0 to n[3] do T[k+2] := solve((k+1)*(k+2)*T[k+2]+p3*(k+1)*(k+2)*Q[k+2]+p1*(sum((m+1)*F[m+1]*T[k-m], m = 0 .. k))-p1*(sum(F[k-m]*(m+1)*T[m+1], m = 0 .. k)), T[k+2]) end do

-(1/2)*p1*a2*a7+(1/2)*p1*al*a8-p3*Q[2]

 

-(1/6)*a2*a7*al*p1^2+(1/6)*a8*al^2*p1^2-(1/3)*al*p1*p3*Q[2]-(1/3)*a3*a7*p1-p3*Q[3]

 

-p3*Q[4]-(1/24)*p1^2*a2^2*a7+(1/24)*a2*p1^2*al*a8-(1/12)*p1*a2*p3*Q[2]-(1/12)*p1*a3*a8-(1/4)*p1*a4*a7-(1/24)*a2*a7*al^2*p1^3+(1/24)*a8*al^3*p1^3-(1/12)*al^2*p1^2*p3*Q[2]-(1/12)*al*a3*a7*p1^2-(1/4)*p1*al*p3*Q[3]

 

(1/120)*(-a*a2*a7*al^3*b*p1^4+a*a8*al^4*b*p1^4-2*a*al^3*b*p1^3*p3*Q[2]-a2*a7*al^3*b*p1^4+a8*al^4*b*p1^4-3*a*a2^2*a7*al*b*p1^3+3*a*a2*a8*al^2*b*p1^3-2*a*a3*a7*al^2*b*p1^3-2*al^3*b*p1^3*p3*Q[2]-6*a*a2*al*b*p1^2*p3*Q[2]-6*a*al^2*b*p1^2*p3*Q[3]-3*a2^2*a7*al*b*p1^3+3*a2*a8*al^2*b*p1^3-2*a3*a7*al^2*b*p1^3+R*a*a2*a5*a7*c*p1-R*a*a6*a7*al*c*p1-4*a*a2*a3*a7*b*p1^2-2*a*a3*a8*al*b*p1^2-6*a*a4*a7*al*b*p1^2-6*a2*al*b*p1^2*p3*Q[2]-6*al^2*b*p1^2*p3*Q[3]+2*R*a2*a3*a7*b*p1-6*R*a4*a7*al*b*p1-12*a*a2*b*p1*p3*Q[3]-24*a*al*b*p1*p3*Q[4]-4*a2*a3*a7*b*p1^2-2*a3*a8*al*b*p1^2-6*a4*a7*al*b*p1^2+2*a^2*a3*a7*p1-2*a^2*a5*a7*p1-12*a*a4*a8*b*p1-12*a2*b*p1*p3*Q[3]-24*al*b*p1*p3*Q[4]-120*a*b*p3*Q[5]-12*a4*a8*b*p1-120*b*p3*Q[5])/(b*(1+a))

(3)

n[4] := 3

for k from 0 to n[4] do Q[k+2] := solve((k+1)*(k+2)*Q[k+2]+p4*(k+1)*(k+2)*Q[k+2]+p2*(sum((m+1)*F[m+1]*Q[k-m], m = 0 .. k))-p2*(sum(F[k-m]*(m+1)*Q[m+1], m = 0 .. k)), Q[k+2]) end do

(1/2)*p2*(a10*al-a2*a9)/(p4+1)

 

(1/6)*p2*(a10*al^2*p2-a2*a9*al*p2-2*a3*a9*p4-2*a3*a9)/(p4+1)^2

 

(1/24)*p2*(a10*al^3*p2^2-a2*a9*al^2*p2^2+a10*a2*al*p2*p4-a2^2*a9*p2*p4-2*a3*a9*al*p2*p4+a10*a2*al*p2-2*a10*a3*p4^2-a2^2*a9*p2-2*a3*a9*al*p2-6*a4*a9*p4^2-4*a10*a3*p4-12*a4*a9*p4-2*a10*a3-6*a4*a9)/(p4+1)^3

 

(1/120)*p2*(a*a10*al^4*b*p2^3-a*a2*a9*al^3*b*p2^3+R*a*a2*a5*a9*c*p4^3-R*a*a6*a9*al*c*p4^3+3*a*a10*a2*al^2*b*p2^2*p4-3*a*a2^2*a9*al*b*p2^2*p4-2*a*a3*a9*al^2*b*p2^2*p4+a10*al^4*b*p2^3-a2*a9*al^3*b*p2^3+3*R*a*a2*a5*a9*c*p4^2-3*R*a*a6*a9*al*c*p4^2+2*R*a2*a3*a9*b*p4^3-6*R*a4*a9*al*b*p4^3+3*a*a10*a2*al^2*b*p2^2-2*a*a10*a3*al*b*p2*p4^2-3*a*a2^2*a9*al*b*p2^2-4*a*a2*a3*a9*b*p2*p4^2-2*a*a3*a9*al^2*b*p2^2-6*a*a4*a9*al*b*p2*p4^2+3*a10*a2*al^2*b*p2^2*p4-3*a2^2*a9*al*b*p2^2*p4-2*a3*a9*al^2*b*p2^2*p4+3*R*a*a2*a5*a9*c*p4-3*R*a*a6*a9*al*c*p4+6*R*a2*a3*a9*b*p4^2-18*R*a4*a9*al*b*p4^2+2*a^2*a3*a9*p4^3-2*a^2*a5*a9*p4^3-4*a*a10*a3*al*b*p2*p4-12*a*a10*a4*b*p4^3-8*a*a2*a3*a9*b*p2*p4-12*a*a4*a9*al*b*p2*p4+3*a10*a2*al^2*b*p2^2-2*a10*a3*al*b*p2*p4^2-3*a2^2*a9*al*b*p2^2-4*a2*a3*a9*b*p2*p4^2-2*a3*a9*al^2*b*p2^2-6*a4*a9*al*b*p2*p4^2+R*a*a2*a5*a9*c-R*a*a6*a9*al*c+6*R*a2*a3*a9*b*p4-18*R*a4*a9*al*b*p4+6*a^2*a3*a9*p4^2-6*a^2*a5*a9*p4^2-2*a*a10*a3*al*b*p2-36*a*a10*a4*b*p4^2-4*a*a2*a3*a9*b*p2-6*a*a4*a9*al*b*p2-4*a10*a3*al*b*p2*p4-12*a10*a4*b*p4^3-8*a2*a3*a9*b*p2*p4-12*a4*a9*al*b*p2*p4+2*R*a2*a3*a9*b-6*R*a4*a9*al*b+6*a^2*a3*a9*p4-6*a^2*a5*a9*p4-36*a*a10*a4*b*p4-2*a10*a3*al*b*p2-36*a10*a4*b*p4^2-4*a2*a3*a9*b*p2-6*a4*a9*al*b*p2+2*a^2*a3*a9-2*a^2*a5*a9-12*a*a10*a4*b-36*a10*a4*b*p4-12*a10*a4*b)/((p4+1)^4*b*(1+a))

(4)

U[1] := sum(F[r]*t^r, r = 0 .. n[1]+4)

p[1] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[1])

U[2] := sum(G[r]*t^r, r = 0 .. n[2]+2)

p[2] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[2])

U[3] := sum(T[r]*t^r, r = 0 .. n[2]+2)

p[3] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[3])

U[4] := sum(Q[r]*t^r, r = 0 .. n[2]+2)

p[4] := subs(R = 1, a = 1, b = 1, c = 1, p1 = 1, p2 = .8, p3 = .1, p4 = .1, U[4])

e1 := subs(t = -1, p[1]) = 0

e2 := subs(t = -1, diff(p[1], t)) = 0

e3 := subs(t = 1, diff(p[1], t)) = -1

e4 := subs(t = 1, p[1]) = 0

e5 := subs(t = -1, p[2]) = 0

e6 := subs(t = 1, p[2]) = 1

e7 := subs(t = -1, p[3]) = 1

e8 := subs(t = 1, p[3]) = 0

e9 := subs(t = -1, p[4]) = 1

e10 := subs(t = 1, p[4]) = 0

j := {e1, e10, e2, e3, e4, e5, e6, e7, e8, e9}

j := solve(j)

sj := evalf(j)

{a10 = -3.476623407, a2 = -5.754056209, a3 = .1776219452, a4 = 11.75811242, a5 = 1.324264301, a6 = -684.5523526, a7 = -.2700369914, a8 = 1.152227714, a9 = 2.191204245, al = 0.3618902741e-1}, {a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916}, {a10 = -4.849411034, a2 = 11.61910224, a3 = -20.01600142, a4 = -22.98820448, a5 = -303.7401922, a6 = -153.4446663, a7 = -7.896832028, a8 = -4.917031955, a9 = -9.645684059, al = 10.13300071}, {a10 = -12.41434918+6.055636678*I, a2 = -6.912869603-3.362489448*I, a3 = -9.364948739-.7062944755*I, a4 = 14.07573921+6.724978896*I, a5 = -106.6284397-3.087774395*I, a6 = 184.4202683+38.56644530*I, a7 = 2.689687372-4.048821750*I, a8 = -4.715343127+5.167588829*I, a9 = 8.474095612-5.785653488*I, al = 4.807474369+.3531472377*I}, {a10 = -8.462156658-37.78952093*I, a2 = -22.10322629+.7748996783*I, a3 = -2.926063539-87.71943544*I, a4 = 44.45645258-1.549799357*I, a5 = 126.1645842+1357.517358*I, a6 = -880.5344239+73.01362458*I, a7 = -96.56841781+19.40514883*I, a8 = -11.30265439-58.49348719*I, a9 = -59.25678527+13.86225901*I, al = 1.588031769+43.85971772*I}, {a10 = 21.28781597+0.9115942334e-2*I, a2 = -2.190767380-.1297694199*I, a3 = 0.4834062985e-1-8.617807139*I, a4 = 4.631534761+.2595388398*I, a5 = -1.070222696-4.103740084*I, a6 = 28.93315819+1.060309794*I, a7 = -.6440073083+2.959900705*I, a8 = 3.178056838-1.712994921*I, a9 = -1.124006374+8.865509135*I, al = .1008296851+4.308903570*I}, {a10 = -2.226772562-4.893664011*I, a2 = -5.213384606-.4953312060*I, a3 = 1.881656676-24.64377975*I, a4 = 10.67676921+.9906624121*I, a5 = -5.922885277-14.38776520*I, a6 = 9.281006594-6.268746147*I, a7 = -8.563253672+2.519226454*I, a8 = -2.293245547-7.112743663*I, a9 = -4.948019289+2.035858706*I, al = -.8158283379+12.32188987*I}, {a10 = -3.311080211+1.380948844*I, a2 = -6.825505968+3.517539795*I, a3 = 10.11566715-.6387142267*I, a4 = 13.90101194-7.035079589*I, a5 = 106.6696011-4.144959139*I, a6 = 183.4179274-43.03852019*I, a7 = -1.117431335-0.4722817327e-1*I, a8 = -1.705921790+.2164542338*I, a9 = -2.431505210+.6185873236*I, al = -4.932833576+.3193571133*I}, {a10 = 1.720689325, a2 = 11.30494181, a3 = 20.89441402, a4 = -22.35988362, a5 = 304.5741226, a6 = -141.0519632, a7 = -3.607319024, a8 = 2.107261122, a9 = -3.764007990, al = -10.32220701}, {a10 = -3.311080211-1.380948844*I, a2 = -6.825505968-3.517539795*I, a3 = 10.11566715+.6387142267*I, a4 = 13.90101194+7.035079589*I, a5 = 106.6696011+4.144959139*I, a6 = 183.4179274+43.03852019*I, a7 = -1.117431335+0.4722817327e-1*I, a8 = -1.705921790-.2164542338*I, a9 = -2.431505210-.6185873236*I, al = -4.932833576-.3193571133*I}, {a10 = -2.226772562+4.893664011*I, a2 = -5.213384606+.4953312060*I, a3 = 1.881656676+24.64377975*I, a4 = 10.67676921-.9906624121*I, a5 = -5.922885277+14.38776520*I, a6 = 9.281006594+6.268746147*I, a7 = -8.563253672-2.519226454*I, a8 = -2.293245547+7.112743663*I, a9 = -4.948019289-2.035858706*I, al = -.8158283379-12.32188987*I}, {a10 = 21.28781597-0.9115942334e-2*I, a2 = -2.190767380+.1297694199*I, a3 = 0.4834062985e-1+8.617807139*I, a4 = 4.631534761-.2595388398*I, a5 = -1.070222696+4.103740084*I, a6 = 28.93315819-1.060309794*I, a7 = -.6440073083-2.959900705*I, a8 = 3.178056838+1.712994921*I, a9 = -1.124006374-8.865509135*I, al = .1008296851-4.308903570*I}, {a10 = -8.462156658+37.78952093*I, a2 = -22.10322629-.7748996783*I, a3 = -2.926063539+87.71943544*I, a4 = 44.45645258+1.549799357*I, a5 = 126.1645842-1357.517358*I, a6 = -880.5344239-73.01362458*I, a7 = -96.56841781-19.40514883*I, a8 = -11.30265439+58.49348719*I, a9 = -59.25678527-13.86225901*I, al = 1.588031769-43.85971772*I}, {a10 = -12.41434918-6.055636678*I, a2 = -6.912869603+3.362489448*I, a3 = -9.364948739+.7062944755*I, a4 = 14.07573921-6.724978896*I, a5 = -106.6284397+3.087774395*I, a6 = 184.4202683-38.56644530*I, a7 = 2.689687372+4.048821750*I, a8 = -4.715343127-5.167588829*I, a9 = 8.474095612+5.785653488*I, al = 4.807474369-.3531472377*I}

(5)

p[1] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[1])

.2586309916+.2575353882*t-.2672619833*t^2-.2650707765*t^3+0.8630991633e-2*t^4+0.7535388242e-2*t^5

(6)

p[2] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[2])

0.7065354871e-1+.1172581545*t+.3439809338*t^2+.3401058738*t^3+0.8536551748e-1*t^4+0.4263597162e-1*t^5

(7)

p[3] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[3])

.6100817436-.5277387253*t-.1364241818*t^2+0.3945483872e-1*t^3+0.2634243820e-1*t^4-0.1171611337e-1*t^5

(8)

p[4] := subs(a10 = -.5218741555, a2 = .2575353882, a3 = -.2672619833, a4 = -.2650707765, a5 = 0.7065354871e-1, a6 = .1172581545, a7 = .6100817436, a8 = -.5277387253, a9 = .5842364534, al = .2586309916, p[4])

.5842364534-.5218741555*t-.1037943244*t^2+0.3134539737e-1*t^3+0.1955787096e-1*t^4-0.9471241840e-2*t^5

(9)

NULL

value*of*D@@2*F(0)*For*R = 1, 1.5, `and`(2*Using*Both*DTM*scheme, dsolve*method)

 

Download DTM_practice.mw

Hi,

It might be really trivial, but I am struggling in the algebraic manipulation of the argument of the exponential function. As an example, I want to substitute 

I*T[0]*(omega1-2*omega2) = I*omega2*T[0]-I*si*T[2]

in the expression of

exp(-I*T[0]*(omega1-2*omega2)).

However, I am only able to do so by subs command and also by exactly copying the argument in the following manner.

subs(-I*T[0]*(omega1-2*omega2) = I*omega2*T[0]-I*si*T[2], exp(-I*T[0]*(omega1-2*omega2)))

The issue is I have expressions like this all over in the main problem, and I have to copy-paste such expressions for the substitution. So I am wondering if there is a more efficient way to tackle this problem. 

Thanks in Advance,

Regards

I'm attempting to visualize temperature averages across a 2 dimentional space (e.g., a square plate) with fixed heat sources. The 3rd dimension (z axis) represents temperature.  I have created several visualizations but have questions about how these plots work.  The model is attached and the questions will make sense once you open the worksheet.

  1. Using the "colorscheme" option on a couple of matrixplots, I get the error "[Length of output exceeds limit of 1000000]" and the plot doesn't show.  However using the "display()" command on those same plots does render the plot.  Is there a way around this error (i.e., rendering the plot directly) or should I just suppress the error using a colon at the end of the plot statement and rely on display() to show the plot?
  2. I've created a heat map as one of the visualizations.  Is there a way to access the color values at each of the "cells" of the heat map? I would like to use these colors elsewhere in the model but I'm not sure if there is a way to access the color values.
  3. Using a 3D point plot as one of the visualization options, I use the colorschemes with options "xgradient", "ygradient", and "zgradient".  For some reason, "xgradient" and "ygradient" work as expected but "zgradient" looks the same as "ygradient".  How do I get the color transition to change along the z axis rather than only x and y axes?

Thank you for your help on these questions.

temperature_profile_(experimental)(v01).mw

Hi,
Apparently I have a problem but I can't find it. Please advise what is the source of the error?
Please see the attached worksheet.
1.mw

restart;
alias(u = u(x, z, t), f = f(x, z, t));
                              u, f
u := (f+sqrt(R))*exp(I*R*x);
                    /     (1/2)\           
                    \f + R     / exp(I R x)
pde1 := I*(diff(u, z))+diff(u, x, x)+diff(u, t, t)+u*abs(u)*abs(u)-(u*abs(u)*abs(u))*abs(u)*abs(u);
    / d   \              / d  / d   \\           
  I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
    \ dz  /              \ dx \ dx  //           

           / d   \                /     (1/2)\  2           
     + 2 I |--- f| R exp(I R x) - \f + R     / R  exp(I R x)
           \ dx  /                                          

       / d  / d   \\           
     + |--- |--- f|| exp(I R x)
       \ dt \ dt  //           

                                                            2
       /     (1/2)\                           2 |     (1/2)| 
     + \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

                                                            4
       /     (1/2)\                           4 |     (1/2)| 
     - \f + R     / exp(I R x) (exp(-Im(R x)))  |f + R     | 

simplify(%);
         / d   \              / d  / d   \\           
       I |--- f| exp(I R x) + |--- |--- f|| exp(I R x)
         \ dz  /              \ dx \ dx  //           

                / d   \                 2             
          + 2 I |--- f| R exp(I R x) - R  exp(I R x) f
                \ dx  /                               

             (5/2)              / d  / d   \\           
          - R      exp(I R x) + |--- |--- f|| exp(I R x)
                                \ dt \ dt  //           

                                               2  
                                   |     (1/2)|   
          + exp(I R x - 2 Im(R x)) |f + R     |  f

                                               2       
                                   |     (1/2)|   (1/2)
          + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                               4  
                                   |     (1/2)|   
          - exp(I R x - 4 Im(R x)) |f + R     |  f

                                               4       
                                   |     (1/2)|   (1/2)
          - exp(I R x - 4 Im(R x)) |f + R     |  R     
collect(%, exp(I*R*x));
  /  (5/2)       / d   \      2       / d   \   / d  / d   \\
  |-R      + 2 I |--- f| R - R  f + I |--- f| + |--- |--- f||
  \              \ dx  /              \ dz  /   \ dx \ dx  //

       / d  / d   \\\           
     + |--- |--- f||| exp(I R x)
       \ dt \ dt  ///           

                                          2  
                              |     (1/2)|   
     + exp(I R x - 2 Im(R x)) |f + R     |  f

                                          2       
                              |     (1/2)|   (1/2)
     + exp(I R x - 2 Im(R x)) |f + R     |  R     

                                          4  
                              |     (1/2)|   
     - exp(I R x - 4 Im(R x)) |f + R     |  f

                                          4       
                              |     (1/2)|   (1/2)
     - exp(I R x - 4 Im(R x)) |f + R     |  R     
 

I see that using units with the maximize() function causes the connection to the kernel to be lost and then Maple (v2018) must be restarted for things to work properly.  This is obviously not desired behavior - is there any known workaround for this issue? (other than forgoing the use of units?).  Attached is a simple worksheet that illustrates this problem.  It has one part without units that works properly and one part with units that causes the error:  Units_Lose_Kernel.mw

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 am using temperature units with thermophysical data and scientific constants but am getting inconsistent behavior when using these.  In some cases (e.g., when calling thermophysical data), it seems that it's best to use a Temperature object.  However I have tried to use scientific constants in calculations and it seems that temperature expressions work best (i.e., when using degrees K rather than deg F or deg C).  Simplifying/combining units don't seem to work when using a Temperature object (or when using expressions with deg F).  It may be something simple I am overlooking but I can't figure out the pattern of behavior yet.  I've attached a file that demonstrates the issue:  Temperature_Object_Use.mw

Thanks for any insight here.

Hi,
I want to find (w/k)^2 from the following Eq. by Maple. How do I do it?
(u0b, mu,deltab,sigma and A are fixed parameters)

Eq.mw

am attaching the worksheet of the problem please help me to solve not able to  compute coupled

error.mw

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