## 90 Reputation

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

## Solving and Plotting PDE...

Maple

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])

## Problem Plotting Stream Function...

Maple MaplePrimes

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 .

## Convert series to function...

Maple

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

## How to convert series functions back to ...

Maple

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.

## Error, (in thaw) numeric exception: divi...

Maple

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.

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