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Hello all,

 

I am trying to solve a simple PDE with one unknow theta and three boundary conditions. Unfortunately, I receive error messages. In this case, the integer s seems to cause troubles. The error message is:

Error, (in pdsolve/numeric/process_PDEs) variable(s) {s} are in the PDE system but are not dependent or independent variables

 

When I assign s a value (such as 1 or 2), no error messages, but still no response. I get:

pds:=module() export plot,plot3d,animate,value,settings; ... end module

Would anyone have an idea how to resolve this issue? Thank you for your suggestions. Below is the small portion of code

restart;
with(PDEtools);

PDE := [(1-y^(s+1))*(diff(theta(y, z), z)) = diff(theta(y, z), `$`(y, 2))+y^(s+1)*(s+1)^(1/s+1)];
IBC := {theta(1, z) = 0, theta(y, 0) = 0, (D[1](theta))(0, z) = 0};

pds := pdsolve(PDE, IBC, numeric);
Error, (in pdsolve/numeric/process_PDEs) variable(s) {s} are in the PDE system but are not dependent or independent variables

Hey people,

 

I am trying to get the following code to run, but it keeps returning an error about too many arguments

 

restart:with(plots):with(PDEtools):
alpha_const := 0.5:gamma_const := 2.5: D1 := 0.05: D2 := 0.002:
A := diff_table(a(x,t)):B := diff_table(b(x,t)):
Selkov[1] := A[t] = 1 - A[]*B[]^(gamma_const) + D1*A[x,x]:
Selkov[2] := B[t] = alpha_const * ( A[]*B[]^(gamma_const) - B[]) + D2 * B[x,x]:

bc[1] := D[1](a)(0,t)=0: bc[2] := D[1](b)(0,t)=0: bc[3] := D[1](a)(4*Pi,t) = 0: bc[4]:=D[1](b)(4*Pi,t)=0:

ic[1] := eval(A[],t=0)=a_0:ic[2] := eval(B[],t=0)=b_0:
case1 := eval(ic,[a_0=1,b_0=1]):
case2 := eval(ic, [a_0=piecewise((x<2*Pi+1) and (x>2*Pi-1), 0.99, 1), b_0=piecewise((x<2*Pi+1) and (x>2*Pi-1), 0.99, 1)]):

Case1Default := pdsolve({Selkov[1],Selkov[2]},{bc[1],bc[2],bc[3],bc[4],case1[1],case1[2]},numerical);


Error, (in pdsolve/sys) too many arguments; some or all of the following are wrong: [{a(x, t), b(x, t)}, {a(x, 0) = 1, b(x, 0) = 1, (D[1](a))(0, t) = 0, (D[1](a))(4*Pi, t) = 0, (D[1](b))(0, t) = 0, (D[1](b))(4*Pi, t) = 0}, numerical]

 

My code worked just earlier today, and now it wont. If i try to run pdsolve({Selkov[1],Selkov[2]}) it says that there is an error with general case of floats. 

 

You help is greatly appreciated!

Trying to solve the 1-dimensional heat equation with maple with constant boundary temperatures:

restart;

with(PDETools):
U := diff_table(u(x,t)):
pde := U[t]=U[x,x];
bc := u(0, t) =0, u(1, t) = 1, u(x,0)=x;
pdsolve([pde,bc]);

The solution of this equation is u(x,t)=x , but pdsolve(...) does not return anything at all! What is going wrong? Is it too hard PDE for maple? And if it is too hard, where can be found the types of equations, which are too hard and not too hard? Thank you.

I'm trying to execute the program, which can be found here http://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/pdsolve_boundaryconditions , but it does not work. I copied exactly what is written there:

restart; with(PDEtools):
U := diff_table(u(x,t)):
pde[1] := U[t]+c*U[x]=-lambda*U[];
bc[1] := eval(U[], t=0) = phi(x);
sys[1] := [pde[1], bc[1]];
pdsolve(sys[1]);

But after last command it just sais that

Error, (in pdsolve/sys/info) found functions with same name but depending on different arguments in the given DE system: [u(x,t), u(x,0)]

What's wrong?

In another experiment with pdsolve, I am solving a PDE with two sets of boundary conditions. Unfortunately, after invoking pdsolve, I get no result at all. What can be wrong here?

Dear All,

i am solving a system of pde with boundar conditons then i got this error...

Error, (in pdsolve/numeric/plot) unable to compute solution for tau>HFloat(0.0):

Thank.

jeffrey_fluid.mw

restart

with(plots):

``

Pr := .71;

.71

 

1

 

1

 

1

(1)

PDE := {(diff(theta(eta, tau), eta, eta))/Pr+f(eta, tau)*(diff(theta(eta, tau), eta))-theta(eta, tau)*(diff(f(eta, tau), eta))-a*(diff(theta(eta, tau), tau)) = 0, diff(f(eta, tau), eta, eta, eta)+f(eta, tau)*(diff(f(eta, tau), eta, eta))-(diff(f(eta, tau), eta))^2-a*(diff(f(eta, tau), eta, tau))-K*(a*(diff(f(eta, tau), eta, eta, eta, tau))+2*(diff(f(eta, tau), eta))*(diff(f(eta, tau), eta, eta, eta))-(diff(f(eta, tau), eta, eta))^2-f(eta, tau)*(diff(f(eta, tau), eta, eta, eta, eta)))+lambda*(1+epsilon*cos(Pi*tau))*theta(eta, tau) = 0};

{1.408450704*(diff(diff(theta(eta, tau), eta), eta))+f(eta, tau)*(diff(theta(eta, tau), eta))-theta(eta, tau)*(diff(f(eta, tau), eta))-(diff(theta(eta, tau), tau)) = 0, diff(diff(diff(f(eta, tau), eta), eta), eta)+f(eta, tau)*(diff(diff(f(eta, tau), eta), eta))-(diff(f(eta, tau), eta))^2-(diff(diff(f(eta, tau), eta), tau))-K*(diff(diff(diff(diff(f(eta, tau), eta), eta), eta), tau)+2*(diff(f(eta, tau), eta))*(diff(diff(diff(f(eta, tau), eta), eta), eta))-(diff(diff(f(eta, tau), eta), eta))^2-f(eta, tau)*(diff(diff(diff(diff(f(eta, tau), eta), eta), eta), eta)))+(1+cos(Pi*tau))*theta(eta, tau) = 0}

(2)

IBC := {f(0, tau) = 0, f(10, tau) = 0, f(eta, 0) = 0, theta(0, tau) = 1, theta(10, tau) = 0, theta(eta, 0) = 0, (D[1](f))(0, tau) = 1, (D[1](f))(10, tau) = 0};

{f(0, tau) = 0, f(10, tau) = 0, f(eta, 0) = 0, theta(0, tau) = 1, theta(10, tau) = 0, theta(eta, 0) = 0, (D[1](f))(0, tau) = 1, (D[1](f))(10, tau) = 0}

(3)

L := [1]

[1]

(4)

for i to 1 do K := L[i]; pds := pdsolve(PDE, IBC, numeric, spacestep = 1/100); p[i] := plots[display]([seq(pds:-plot(f, tau = 1, eta = 0 .. 1, legend = L[i]), j = 5)]) end do

1

 

module () local INFO; export plot, plot3d, animate, value, settings; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; end module

 

Error, (in pdsolve/numeric/plot) unable to compute solution for tau>HFloat(0.0):
Newton iteration is not converging

 

display({p[1]})

Error, (in plots:-display) expecting plot structures but received: {p[1]}

 

``

 

Download jeffrey_fluid.mw

test.mw

In this file, I tried my best to solve the pde. But the answer is still rather non-informative. I need some help to simplify it.

I did notice that my Maple might need reinstallation, due to a "bug" in the 18.02 update.

 

My ultimate aim is try to use some similar techniques to solve this, test2.mw, which has a similar type pde.

 

The standard pdsolve(pde) would just not work.

 

UPDATE:

I used the same file in Maple 17 on a differnt Machine, which can be solved by pdsolve. So I guess it's just that  the 18.02 update package is broken itself. I have tried to uninstall and reinstall twice.

 

 

Thanks,

 

casper

PD := [diff(Th(z, t), t) = 7.1428*(diff(Th(z, t), z))-1397941.885*(279-Tw(z, t))-0.2160487e-1*(diff(Th(z, t), z, z)), diff(Tc(z, t), t) = -7.1428*(diff(Tc(z, t), z))+1298990.852*(Tw(z, t)-291)+0.189366e-1*(diff(Tc(z, t), z, z)), diff(Tw(z, t), t) = 3.3024901*(Th(z, t)-2*Tw(z, t)+Tc(z, t))+8.0029*10^(-4)*(diff(Tw(z, t), z, z))]

BCI := {Tc(0, t) = 275, Tc(z, 0) = 275, Th(1, t) = 296, Th(z, 0) = 296, Tw(0, t) = 0, Tw(z, 0) = 0, (D[1](Tc))(1, t) = 0, (D[1](Th))(0, t) = 0, (D[1](Tw))(1, t) = 0}

pds := pdsolve(PD, BCI, numeric)

Hello,

Since I was working in Matlab with Galerkin method which implies periodic boundary conditions I was wondering how to implement this in maple.

I tried this:

restart;

pde2 := diff(u(x, t), t)+3*(diff(u(x, t)^2, x))+diff(u(x, t),x$3) = 0

IBC := {u(0, t) = u(2, t), u(x, 0) = sech(50*(x-1/2))^2+2*sech(30*(x-1))^2, (D[1](u))(0, t) = (D[1](u))(2, t), (D[2](u))(0, t) = (D[2](u))(2, t)}

pds := pdsolve(pde2, IBC, numeric, time = t, range = 0 .. 2)

But it's telling me: 

Error, (in pdsolve/numeric/process_IBCs) initial/boundary conditions can only contain derivatives which are normal to the boundary, got (D[2](u))(0, t)

So what's wrong?

declare(W(x, y), Z(x, y));

 

sys := [-A*kappa3-`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(x))*(2*G-A)/`&PartialD;`(x)-2*G*(`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(y))/`&PartialD;`(y)+`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(y))+A*`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(y) = 0, `&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(y))*(A-4*G)/`&PartialD;`(y)+`&PartialD;`(`&PartialD;`(W(x, y))/`&PartialD;`(x))*(A-2*G)/`&PartialD;`(y)-2*G*`&PartialD;`(`&PartialD;`(Z(x, y))/`&PartialD;`(x))/`&PartialD;`(x) = 0];

 

I have this system of coupled PDE and I wish to solve it using Maple.

It gives me error of this kind:

 

pdsolve(sys, [[W(x, y)], [Z(x, y)]]);


Error, (in pdsolve/sys) found functions depending on different variables in the given DE system: [`&PartialD;`(x), `&PartialD;`(y)]

 

Thanks a lot for help

I'm taking my first steps with maple and pdsolve, trying to run the example in the maplesoft support page:

http://www.maplesoft.com/support/help/Maple/view.aspx?path=examples/pdsolve_boundaryconditions

which reads

>
> restart; with(PDEtools);
> U := diff_table(u(x, t));
>

and I get a solution that is different from the web page, and when i run

Im using maple 13. Any tips about what's wrong?

 

regards

restart:with(plots):with(PDEtools):

 pde:=1/r*diff(r*diff(U(r,z),r),r)+1/b^2*diff(U(r,z),z,z)=0;

ans := pdsolve(pde);

ics:=(D[1](U))(0, z) = 0,(D[2](U))(r, 0)-B*U(r,0) = 0;

bcs:=(D[2](U))(r, 1)+B*U(r,1) = B,(D[1](U))(1, z)+B*U(1,z) = 0;

B:=1:b:=1:

S:= pdsolve(pde, {bcs, ics}, numeric);

Error, (in pdsolve/numeric) unable to handle elliptic PDEs

anyway around this?

 

RIZPDE.mw

Dear all,

I tried to use pdsolve to solve the parabolic pde but get the unexpected answer:

Is it the PDESolStruc or the other structure? Where can I find the description about this kind of structure.

Thanks.

Hello everyone,

i'm trying to simulate a diffusion problem. It contains two connected regions in which a species is diffusing at different speeds. In one region (zeta) one boundary is set to be constant whereas in the other region (c) there is some oscillation at the boundary.The code i try to use is as follows:

sys1 := [diff(c(x, t), t) = gDiffusion*10^5*diff(c(x, t), x$2), diff(zeta(x, t), t) = KDiffusion*10^6*diff(zeta(x, t), x$2)]

pds := pdsolve(sys1, IBC, numeric, time = t, range = 0 .. 3000, spacestep = 3)

However the main problem are my boundary conditions:

IBC := {c(0, t) = 0, c(x > 0, 0) = 0, zeta(0, t) = .4, zeta(x > 0, 0) = .4, (D[1](c))(3000, t) = sin((1/100)*t), (D[1](zeta))(0, t) = 0}

Like this it principally works (however it is apparently ill-posed).

Now what i do like is that the two equations are coupled at x=2000 with the condition that c(2000,t)=zeta(2000,t). This however i dont seem to be able to implement.

I appreciate your comments

Goon

why system inconsistent 

when only want to obtain a equation H

in terms of a1 , a3, b2, b3, c1, c2, x1, x2, lambda

pdsolve([
Diff(H(x1,x2,lambda), x1) = a1*x1 + a3*lambda,
Diff(H(x1,x2,lambda), x2) = b2*x2 + b3*lambda,
Diff(H(x1,x2,lambda), lambda) = c1*x1 + c2*x2
], H(x1,x2,lambda));

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