# Items tagged with pdepde Tagged Items Feed

### Symmetries of strange PDE...

June 29 2016
2 11

I thought about the following PDE:

EDIT: The u(0,t) is not a typo! It is really meant to be part of the PDE!

Latex/Matjax: $$\dfrac{\partial u(x,t)}{\partial t}=\alpha \dfrac{\partial^2 u(x,t)}{\partial x^2}+u(x=0,t).$$

Maple: diff(u(x,t),t)=alpha*diff(u(x,t),x$2)+u(0,t) How can i determine the symmetries of this PDE with Maple? ### How to write boundary condition in pdsolve?... June 21 2016 1 4 I have the PDE u_{xx}+u_{yy} = 1 with BC: u|_{x^2+y^2=1} =0 ; how to write down the command of the BC in solving this PDE?, btw can I make maple show me how to solve this PDE analytically? Thanks in advance. Here are the lines that I wrote so far: pde := diff(u(x, y), x, x)+diff(u(x, y), y, y) = 1; ans := pdsolve(pde) how to add the BC correctly to pdsolve? I am not sure how to write the condition x^2+y^2=1 and that u will get a value on this boundary. ### Solve PDE by Maple... June 20 2016 0 6 Hi all, Please help me with this question. I want to solve a PDE by Maple.  (1)  (2)  (3)  (4) ### How to solve this PDE system?... June 19 2016 0 6 hi .please help me for solve this equations. bbb2.mw  (1)  (2)  (3)  (4)  (5) if former equations are not solvable , please help me for another way, in which at first two equation solve..in this way in equation [J and B] assume that q[311]=e[311]=0 and dsolve perform to find Φ and ψ after by finding Φ and ψ is use for detemine w and u0 please see attached file below[bbb2_2.mw] bbb2_2.mw Download bbb2.mw ### Problem with PDE solution ... June 08 2016 1 8 vz := 2*(-eta^2+1); D_im := .22; r0 := 1; pde := diff(vz*Y(eta, z), z)-D_im*((diff(eta*(diff(Y(eta, z), eta)), eta))/eta+diff(Y(eta, z), $(z, 2)))/r0 = 0;

pde := expand(%);

ibc := [Y(1, z) = 0, (D[1](Y))(0, z) = 0, Y(eta, 0) = 1, (D[2](Y))(eta, 0) = 0];

sol := pdsolve(pde, ibc, numeric, time = z, range = 0 .. 1);

pds := sol:-value(z = 0, output = listprocedure);

sol:-plot(z = 0.1e-3, numpoints = 50, color = blue, view = 0 .. 1)

So I was trying to solve this conservation equation for the radial coordinate eta and the z coordinate being treated as time. The flow is in z direction. Now unfortunately it is diverging. Not sure why though. What am I doing wrong?

### How to solve this PDE problem?...

May 22 2016
0 5

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hai All,

i have problem to soilve pde in the maple

can anyone suggest / idea to solve in maple?

### PDE system ...

May 07 2016
0 3

I am currently working on FDM ,i have 2 coupled nonlinear pde ,i need help in solving these equation using maple code.

> restart:

> alias(f=f(tau,eta), theta=theta(tau,eta));

>

> PDE1:=S*diff(f,tau,eta)=eta^2*diff(f,eta)^2+(6*eta^2-2*f*eta)*diff(f,eta)+(6*eta^3-f*eta)*diff(f,eta,eta)-eta^4*diff(f,eta,eta,eta);

> PDE2:=eta^4*diff(theta,eta,eta)+2*eta^3*diff(theta,eta)-Pr*(f*eta^2*diff(theta,eta)+S*diff(theta,tau))=0;

### Error when using pdsolve...

May 04 2016
1 7

I'm trying to solve a 2nd order system of pde's with couplded BC but it gives me the following error

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

Here is the code

> T01 := 273; T02 := 26; L1 := .1; L2 := .2; h1 := 100; h2 := 200; k1 := 1; k2 := 2; rho1 := 1000; rho2 := 2000; c1 := 0.1e6; c2 := 0.2e6; alpha1 := 1; alpha2 := 2

> PDE := {diff(T1(x, t), t) = (diff(T1(x, t), x, x))/alpha1, diff(T2(x, t), t) = (diff(T2(x, t), x, x))/alpha2}

> IBC:={k1*(D[1](T1))(L1, t) = k2*(D[1](T2))(L1, t), T1(L1, t) = T2(L1, t), T1(x, 0) = T02, T2(x, 0) = T02, (D[1](T1))(0, t) = -h1*(T1(0, t)-T01)/k1, (D[1](T2))(L1+L2, t) = h2*(T2(L1+L2, t)-T02)/k2}

> pds := pdsolve(PDE, IBC, numeric)

Its basically a 1D heat equation in a 2 layers plate with conduction BC on both sides

### How to solve a nonlinear PDE system?...

April 16 2016
0 3

I am currently working on FDM ,i have 2 coupled nonlinear pde ,i need help in solving these equation using maple code.

> restart:

> alias(f=f(tau,eta), theta=theta(tau,eta));

>

> PDE1:=S*diff(f,tau,eta)=eta^2*diff(f,eta)^2+(6*eta^2-2*f*eta)*diff(f,eta)+(6*eta^3-f*eta)*diff(f,eta,eta)-eta^4*diff(f,eta,eta,eta);

> PDE2:=eta^4*diff(theta,eta,eta)+2*eta^3*diff(theta,eta)-Pr*(f*eta^2*diff(theta,eta)+S*diff(theta,tau))=0;

### Modelling solitons...

March 29 2016
1 6

Hi guys, I'm currently having a lot of trouble with Maple and can't seem to get stuff to work. I have the task of solving and modelling the Klien Gordon equation, with a chosen potential. The equation I'm trying to solve is:

> KGE := diff(psi(x, t), x, x)-(diff(psi(x, t), t, t))-12*psi(x, t)^5+10*psi(x, t)^4+6*psi(x, t)^3-3*psi(x, t)^2-psi(x, t) = 0

I'm doing this by changing the pde into an ode via a transformation

>tr := {t = tau, x = c*tau+z, psi(x, t) = U(z)}

>ode1 := dchange(tr, KGE, [z, tau, U(z)])

>ode1 := collect(ode1, diff(U(z), z, z))

>c := 1/4

>ode2 := subs({U(z) = U, diff(U(z), z, z) = V(U)*(diff(V(U), U))}, ode1)

>sol := dsolve({ode2, V(0) = 0}, V(U))

>sol1:= sol[2]

>z := -c*t+x = int(1/rhs(sol2), U)

>solwave := psi(x, t) = solve(z, U)

I then checked if my solution, solwave actually solved the pde via pdetest(solwave,KGE) and it did. Hence this is what I took as one of the kinks. Although the kink solution looks hideous and I have no idea how to try and take the limit as x goes to infinity, as to show it tends to a vacuum of the potential. I've tried taking the limit but all Maple does is replace all the x with infinity signs...

I then tried animating it to see if it worked, but it just looks wrong, there are breaks within the curve and also very random spikes which I cannot explain at all..

I tried this code exactly for the Sine Gordon equation and it works perfectly, it just all goes wrong when I try to change the potential.

Here is a picture of the frame:

----------------------------------------------------------------------------------------------

Another issue I had was with dealing with the potential on it's own, every time I try inputting

>1/2(u^2)(1-u)^2(1+2u)^2

into maple it changes the expression into something completely different and wrong, it somehow comes out with an exponential of 8.. This is what I get:

(1/2)*(u(1-u))(1+2*u)^8

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I also have a problem integrating, I try and plug in a value, i.e.

>int(1/(x(1-x))(1+2*x), x)

but all this does is show me what I inputted but with a integral sign...

I'm very very new to Maple and have spent over a week doing this, but it just isn't working out at all :( Please help!!

### Second order PDE system...

March 09 2016
0 3

 (1)

Hi all,

I have the following PDE, is it solveable by Maple or not. Do I need a boundary condition and how many or I can get a general solution? I am new to Maple. Any help will be appreciated.

Thank you.

### Solve a System of Partial Differential Equations...

March 07 2016
1 2

Hello,

I am new to Maple. I am working on PDE and I wanted to try an easy example to know how to work with Maple. So, I startted with the example from the HELP, but still get error as shown below. Can someone guides me.

Thank you.

### Exporting plot data to MATLAB...

February 10 2016
1 10

Hello all,

I am pretty new to Maple, but I am trying to understand something. I was able to find a numerical solution to a PDE in maple (with some community help, thanks guys!). I am trying to manipulate this data but am struggling with it. I thought if I could take this data to matlab it would be pretty easy for me to manipulate and do what I want.

So my question is: How do I export my numerical solution (pds module) to matlab. Just taking the data is okay. I know you can evaluate the data at some points.

I see there is "Matlab" command that converts code, it doesn't seem to like pds as an input though.

I also see an export matrix command. I guess it could be possible to create a matrix of plot data and convert it this way?

I had to do a change of coordinate system to solve the PDE because of boundary conditions. I'm trying to transform this data back to my regular x,y coordinate system to see if it matches some other simulations.

Thanks in advance! And here is my file.

restart;
with(Physics):
Setup(mathematicalnotation = true):

V(Z, f);

If function ( varphi) is defined, use this one.

PDE1 := subs[inplace](x = xi*varphi(t), PDE1);
If function ( varphi) is defined, use this one.

PDE1 := subs[inplace](t = 2*vartheta*(1/omega), PDE1);

Thesis_Pde2_attempt.mw

### Plot of the difference between solutions...

February 05 2016
0 4

I have the following code:

restart;
PDE := diff(u(x, t), t) = diff(u(x, t), x, x)-sin(x+t)+cos(x+t);
IBC:= D[1](u)(0,t)=-sin(t),
D[1](u)(1,t)=-(u(1, t))^4+(cos(1+t))^4-sin(1+t),
u(x,0)=cos(x);

pds := pdsolve( PDE, [IBC], numeric, time = t, range = 0 .. 1,

spacestep = 0.1e-1, timestep = 0.1e-1,
errorest=true
)

And I want to plot the difference |pds(t,x) - cos(x+t)| in maple for x=1 and t=0..5

I thought to use the following piece of commands but I get an error:

P:=unapply(pds, t,x);
Q:=abs(P(t,x)-cos(x+t));
Q:-plot(x=1, t=0..1);

I get an error that Q isn't a module.

I thought that unapply is used for this case, can you help me with this simple task?

### Change PDE into ODE...

January 15 2016
1 5

PLEASE..!! CAN ANYONE HELP ME IN CODING ON MAPPLE 13 TO CHANGE PDE INTO ODE??

MY FUNCTION IS THIS

U[t, t]-U[t, t, x, x]-(aU[]-b*U[]^3)[x, x] = 0

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