kencom1

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6 years, 246 days
UNIVERSITY OF LAGOS, AKOKA YABA, LAGOS
LAGOS, Nigeria

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These are questions asked by kencom1

Having difficulties solving pde. Below is the problem and its not plotting. Anyone with useful informations. Please

restart;
with(PDEtools, casesplit, declare);
with(DEtools, gensys);
with(Physics);

PDE := diff(theta(x, t), x, x)+beta*theta(x, t)*(diff(theta(x, t), x, x))+beta*((diff(theta(x, t), x))^2)-M^2*theta(x, t)-S[h]*(theta(x, t)^2)+M^2*G*(1+E*theta(x, t))-P[e]*(diff(theta(x, t), x)) = diff(theta(x, t), t);
/ d  / d             \\
|--- |--- theta(x, t)||
\ dx \ dx            //

                      / d  / d             \\
   + beta theta(x, t) |--- |--- theta(x, t)||
                      \ dx \ dx            //

                           2                                     
          / d             \     2                               2
   + beta |--- theta(x, t)|  - M  theta(x, t) - S[h] theta(x, t) 
          \ dx            /                                      

      2                              / d             \    d  
   + M  G (1 + E theta(x, t)) - P[e] |--- theta(x, t)| = --- 
                                     \ dx            /    dt 

  theta(x, t)
BC := theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1;
     theta(x, 0) = 0, Dt(theta(0, t)) = 0, theta(1, t) = 1
Codes := [beta = .1, M = .1, S[h] = .1, G = .1, P[e] = .1, E = .1];
S1 := pdsolve({BC, subs(Codes, PDE)});
PDEplot(S1, [[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, x = 0 .. 1, iterations = 2, numchar = [10, 10], stepsize = 0.5e-1, numsteps = [-5, 5]);
   PDEplot([[t, theta(x, t)], [x, theta(x, t)]], t = 0 .. 1, 

     x = 0 .. 1, iterations = 2, numchar = [10, 10], 

     stepsize = 0.05, numsteps = [-5, 5])

 

Good day sirs,

I am trying to plot graphs on stream function but its given me a lot of multiple error using my codes. Anyone with useful information should please share. 

Below is the code.

Thanks

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/Test.mw .
 

Download Test.mw

Good day everyone,

I'm trying to convert a series solution back to its original function but its given me "Error, (in rsolve/linindex) invalid subscript selector".

Anyone with useful informations please.

Attached is the series below

 

theta := convert(a-(1/2)*beta*a^2*y^2+(1/12)*beta^2*a^3*y^4-(1/72)*beta^3*a^4*y^6+(1/504)*beta^4*a^5*y^8-(5/18144)*beta^5*a^6*y^10+(1/27216)*beta^6*a^7*y^12-(95/19813248)*beta^7*a^8*y^14+O(y^16), polynom);
     1       2  2   1      2  3  4   1      3  4  6
 a - - beta a  y  + -- beta  a  y  - -- beta  a  y 
     2              12               72            

       1      4  5  8     5       5  6  10     1       6  7  12
    + --- beta  a  y  - ----- beta  a  y   + ----- beta  a  y  
      504               18144                27216             

         95        7  8  14
    - -------- beta  a  y  
      19813248             
L := [seq(coeff(theta, y, n), n = 0 .. 14)];
  [        1       2     1      2  3       1      3  4     
  [a, 0, - - beta a , 0, -- beta  a , 0, - -- beta  a , 0, 
  [        2             12                72              

     1      4  5         5       5  6       1       6  7     
    --- beta  a , 0, - ----- beta  a , 0, ----- beta  a , 0, 
    504                18144              27216              

         95        7  8]
    - -------- beta  a ]
      19813248         ]
with(gfun);
rec := listtorec(L, u(n));
[ //      2     2  3         2     2  2          2     2  \        
[{ \2151 a  beta  n  - 1434 a  beta  n  - 30592 a  beta  n/ u(n) + 
[ \                                                                

  /             3                  2                  
  \2476 a beta n  - 137904 a beta n  + 207248 a beta n

                  \         
   + 424320 a beta/ u(n + 2)

     /         3           2                      \           
   + \-153660 n  - 322920 n  + 1803360 n + 2545920/ u(n + 4), 

                               1       2          \      ]
  u(0) = a, u(1) = 0, u(2) = - - beta a , u(3) = 0 }, ogf]
                               2                  /      ]

rsolve(rec[1], u);
      / //      2     2  3         2     2  2          2     2  \ 
rsolve|{ \2151 a  beta  n  - 1434 a  beta  n  - 30592 a  beta  n/ 
      \ \                                                         

         /             3                  2                  
  u(n) + \2476 a beta n  - 137904 a beta n  + 207248 a beta n

                  \         
   + 424320 a beta/ u(n + 2)

     /         3           2                      \           
   + \-153660 n  - 322920 n  + 1803360 n + 2545920/ u(n + 4), 

                               1       2          \    \
  u(0) = a, u(1) = 0, u(2) = - - beta a , u(3) = 0 }, u|
                               2                  /    /
sum(%*y^n, n = 0 .. infinity);
Error, (in rsolve/linindex) invalid subscript selector

thanx

 

Good morning sirs,

Anyone with the idea(s) on how to convert series back to its original form should please share with me. 

Take for example

a-(1/2)*beta*a^2*y^2+(1/24)*beta^2*a^3*y^4-(1/720)*beta^3*a^4*y^6+(1/40320)*beta^4*a^5*y^8-(1/3628800)*beta^5*a^6*y^10+(1/479001600)*beta^6*a^7*y^12-(1/87178291200)*beta^7*a^8*y^14+O(y^16)

is a series for a*cos(sqr(a*beta)*y)

Thanking you in anticipation for your answer.

Please sir,

I am trying to solve this problem and is giving me the error code "Error, (in thaw) numeric exception: division by zero
". Anyone with useful informations please.

Thanking you in anticipations for your response. 

restart

h := proc (x) options operator, arrow; 1+x*tan(theta)/delta+phi*sin(2*Pi*x) end proc:

A := M*(1+K):

theta[1] := sqrt((-B+sqrt(-4*A*C+B^2))/(2*A)):

xi := H[a]^2+(1+K)/K[p]:

L := xi[1]*cosh(theta[1]*h(x))+beta*xi[1]*theta[1]*sinh(theta[1]*h(x))*sinh(theta[2]*h(x))-xi[2]*cosh(theta[2]*h(x))-beta*xi[2]*theta[2]*sinh(theta[2]*h(x))*sinh(theta[1]*h(x)):

F := proc (x) options operator, arrow; (2*xi[1]/theta[1]-2*xi[2]/theta[2])*sinh(theta[1]*h(x))*sinh(theta[2]*h(x))-2*L*h(x) end proc:

w := S*(sinh(theta[1]*y)*sinh(theta[2]*h(x))-sinh(theta[2]*y)*sinh(theta[1]*h(x)))/(L*xi):

u := S*(xi[1]*cosh(theta[1]*y)*sinh(theta[2]*h(x))-xi[2]*cosh(theta[2]*y)*sinh(theta[1]*h(x))-L)/(L*xi)-1:

psi := S*(xi[1]*sinh(theta[1]*y)*sinh(theta[2]*h(x))/theta[1]-xi[2]*sinh(theta[2]*y)*sinh(theta[1]*h(x))/theta[2]-L*y)/(L*xi)-y:

q := int(u, y = -h(x) .. h(x)):

"(∂P)/(∂x):=((q+2*h(x))*L*xi)/(F(x)):"

Error, recursive assignment

 

"Deltap:=(∫)[0]^(1)(∂P)/(∂x) ⅆx"


 

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