## How to get asymptotic solutions?...

Asked by:
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> restart; with(PDETools), with(plots);
> n := .3; Pr := 7; Da := 0.1e-4; Nb := .1; Nt := .1; tau := 5;
> Eq1 := (1-n)*(diff(f(x, y), `\$`(y, 3)))+(1+x*cot(x))*f(x, y)*(diff(f(x, y), `\$`(y, 2)))-(diff(f(x, y), y))/Da+(diff(f(x, y), y))^2+n*We*(diff(f(x, y), `\$`(y, 2)))*(diff(f(x, y), `\$`(y, 3)))+sin(x)*(theta(x, y)+phi(x, y))/x = x*((diff(f(x, y), y))*(diff(f(x, y), y, x))+(diff(f(x, y), `\$`(y, 2)))*(diff(f(x, y), x)));
> Eq2 := (diff(theta(x, y), `\$`(y, 2)))/Pr+Nt*(diff(theta(x, y), y))^2/Pr+Nb*(diff(phi(x, y), y))*(diff(theta(x, y), y))/Pr+(1+x*cot(x))*f(x, y)*(diff(theta(x, y), y)) = x*((diff(f(x, y), y))*(diff(theta(x, y), x))+(diff(theta(x, y), y))*(diff(f(x, y), x)));
> Eq3 := Nb*(diff(phi(x, y), `\$`(y, 2)))/(tau*Pr)+Nt*(diff(theta(x, y), `\$`(y, 2)))/(tau*Pr)+(1+x*cot(x))*f(x, y)*(diff(phi(x, y), y)) = x*((diff(f(x, y), y))*(diff(phi(x, y), x))+(diff(phi(x, y), y))*(diff(f(x, y), x)));
> ValWe := [0, 5, 10];
> bcs := {Nb*(D[2](phi))(x, 0)+Nt*(D[2](theta))(x, 0) = 0, f(0, y) = ((1/12)*y)^2*(6-8*((1/12)*y)+3*((1/12)*y)^2), f(x, 0) = 0, phi(0, y) = -.5*y, phi(x, 12) = 0, theta(0, y) = (1-(1/12)*y)^2, theta(x, 0) = 1, theta(x, 12) = 0, (D[2](f))(x, 0) = Da^(1/2)*(D[2, 2](f))(x, 0)+Da*(D[2, 2, 2](f))(x, 0), (D[2](f))(x, 12) = 0};
> pdsys := {Eq1, Eq2, Eq3}; for i to 3 do We := ValWe[i]; ans[i] := pdsolve(pdsys, bcs, numeric) end do;
> p1 := ans[1]:-plot(theta(x, y), x = 1, color = blue); p2 := ans[2]:-plot(theta(x, y), x = 1, color = green); p3 := ans[3]:-plot(theta(x, y), x = 1, color = black);
> plots[display]({p1, p2, p3});```

## Final solution not visible...

Asked by:

I'm trying to solve Laplace's equation in Maple in 2-D domain. But while writing the last line "pdsolve(pdef)" (to get the final solution) and after that hitting enter, it doesn't shows anything. Please help me regaring this.

## Solving and Plotting PDE...

Asked by:

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 ...

Asked by:

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);
 >

Download PDE_problem.mw

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

Asked by:

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 ...

Asked by:

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 ...

Asked by:

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]

could you please help me?

what is the problem?

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

Asked by:

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...

Asked by:

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?

Please excuse my bad English
thanks

## Parabolic PDE ...

Asked by:

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? ...

Asked by:

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

## PDE numeric BVP how to solve and guess initial con...

Asked by:

Please help me on this :

 >
 >
 >
 >
 >
 >
 >
 >
 >
 >
 >

Download untitle_2_(1).mw

## PDEtools build ...

Asked by:

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...

Asked by:

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...

Asked by:

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?

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