## Solving and Plotting PDE...

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 with PDE ...

what's the problem with PDE below? tnx for help

 > restart:
 > PDE:=diff(u(x,t),t)=k*diff(u(x,t),x\$2)-h*u(x,t);
 (1)
 > IBC := {u(-Pi,t)=u(Pi,t), (D[1](u))(-Pi, t) = (D[1](u))(Pi, t),u(x,0)=sin(x)};
 (2)
 > pdsolve(PDE,IBC);
 >

## Exact symbolic solution of a system of partial dif...

Hi Everybody,

I have a simple question: Does Maple solve systems of partial differential equations with boundary conditions?

Can somebody give me an example?

I have only found numerical solutions to this kind of systems but no symbolic example.

Thanks a lot for yor help.

## finite difference and 2 d plot ...

Hello

I would like to solve the two dimensional heat equation in the square [-1,1]^2  using finite difference.

The following code  does not gives me the right answer.

I appreciate any help

heat2dequation.mw

## plot the solution of a complex PDE equation ...

Hello

I solved a complex PDE equation in maple but I can not plot the output.

The manner was like bellow:

PDE := [diff(A(z, t), z)+(1/2)*alpha*A(z, t)+(I*beta[2]*(1/2))*(diff(A(z, t), t, t))-(I*beta[3]*(1/6))*(diff(A(z, t), t, t, t))-I*(GAMMA(omega[0]))(abs(A(z, t))^2*A(z, t)) = 0];
IBC := {(D[2](A))(z, 1), A(0, t) = -sin(2*Pi*t), A(z, 0) = sin(2*Pi*z), (D[2](A))(z, 0) = 2*z};
pds := pdsolve(PDE, IBC, type = numeric, time = t, range = 0 .. 1);
pds:-plot3d(A(z, t)*conjugate(A(z, t)), t = 0 .. 1, z = 0 .. 10, shading = zhue, axes = boxed, labels = ["x", "t", "A(z,t)"], labelfont = [TIMES, ROMAN, 20], orientation = [-120, 40]);

It is solved but there is an error like:

Error, (in pdsolve/numeric/plot3d) unable to compute solution for z>INFO["failtime"]:
unable to store 11.2781250000000+4390.00000040000*I when datatype=float[8]

what is the problem?

## How to solve a simple PDE?...

I want to solve the system of differential equations
sys :=
diff(x(t,s),t) = y(t,s),
diff(y(t,s),t) + x(t,s) = 0;

subject to the initial condition
ic := x(0,s) = a(s),
y(0,s) = b(s);

where a(s) and b(s) are given.

This looks like a system of PDEs but actually it is a system
of ODEs because there are no derivatives with respect to s.
It is easy to obtain the solution by hand:

x(t,s) = b(s)*sin(t) + a(s)*cos(t)
y(t,s) = b(s)*cos(t) - a(s)*sin(t)

I don't know how to get this in Maple, either through dsolve()
or pdsolve().

Actually both dsolve({sys}) and pdsolve({sys}) do return
the correct general solution, however dsolve({sys, ic})
or pdsolve({sys, ic}) produce no output.  Is there a trick
to make the latter work?

## Partial differential equation...

hi
I want to solve a pde equation:

```equa1 := diff(u(x,y), x, x)-y(1+x) = 0;

# with codition:

con:=u(0,y) = 0, (D(u[x]))(0,y) = 0;
```

the anwer must be :    u(x,y)= y(x2/2  + x3/6)
How can i solve that with maple?

thanks

## Parabolic PDE ...

I am looking for a numerical solver for a parabolic PDE (up to 2nd order derivatives but no mixed ones) on the spatio-temporal domain [X x Y x T], either as an external package or as MAPLE code.

I have coded the method of lines on the domain [X x T] and indeed also used pdsolve as a check for that case. However, pdsolve (numerical) cannot solve the PDEs on the domain [X x Y x T].  The run times and memory requirements for the latter case would of course be significantly greater.

I am about to code up the method of lines (in MAPLE) on the domain [X x Y x T], but am wondering whether there exist external FORTRAN or C code packages that would be faster if called up in MAPLE and whose results would then be post-pocessed in MAPLE.

Does anyone have any suggestions?

MRB

## How to find infinitesimals of a system of pdes? ...

How to find infinitesimals of a system of pdes? I can find out for a single pde but not able able to solve for system of pdes with several dependent and independent variables. Can anyone please provide me the code for that or give some clue. Thanks

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

## PDEtools build ...

What's wrong here?

restart; with(PDEtools); PDE2 := diff(u(x, y, t), t\$2) = diff(u(x, y, t), x\$2)+diff(u(x, y, t), y\$2); IBC2s := u(x, 0, t) = 0, u(x, 2, t) = 0, u(0, y, t) = 0, u(4, y, t) = 0, u(x, y, 0) = (.1*(-x^2+4*x))*(-y^2+2*y), (D[3](u))(x, y, 0) = 0; Sol2 := pdsolve({IBC2s, PDE2}); build(Sol2);

Error, invalid input: PDEtools:-build uses a 1st argument, ANS (of type {`=`, PDESolStruc}), which is mis

## Can I numerically solve a PDE set with one initial...

I am wondering if I can use MAPLE to solve PDE set with one initial value problem for "q" and a boundary condition problem for "p". "q" need to be integrated over time, and for each time step, after updating "q", I need to solve poisson equation for "p":

diff(q(x,y,t),t)=-diff(p(x,y,t),x)*diff(q(x,y,t),y)/cos(xy)+diff(p(x,y,t),y)*diff(q(x,y,t),x)/cos(y)+b*cos(y)^2*diff(p(x,y,t),x)+F(x,y)

diff(p(x,y,t),x,x)+diff(p(x,y,t),y,y)+c(y)*p(x,y,t)=q(x,y,t)

IC: q(x,y,0)=q0(x,y)

BC: periodic in x, second type BC in y.

Many Thanks!

Wanying

## Solution of PDE...

I am trying to see the solution to a PDE that I am coding with initial and boundary conditions. I know with the ODE, it shows the solution, but with the PDE I cannot seem to see it. Any suggestions?

## Heat equation with left end fixed flux and right e...

hello,I want to solve a quesstion about heat equation,that the quesstion like this:

I use the code like this

but the results is wrong obviously and what's wrong with this code?