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Dear all

I have a PDE and its analytical solution. I want to find the numerical solution by Finite Difference Method.

I duscratize the PDE and boundary condition and Could not able to solve them togethe.

Here is the file FEM-Nu.mw


Please, I need assistance with this problem.

Here is the problem I am trying to solve:

restart:
with(plots):
with(LinearAlgebra):
with(PDEtools):
with(Student):

myPDE1 := D11*diff(w(x,y), x$4) + 2*(D12+2*D66)*diff(w(x,y), y$4) + D22*diff(w(x,y), x$2, y$2) - G*diff(w(x,y), x,y)= 0;

pdsolve(myPDE1);

pdsolve(myPDE1, build);

"Boundary conditions";
"(Note:the domain for the problem is a rectangle)";
bc1 := w(0,y) = 0; # @ x=0 edge;
bc2 := w(a,y) = 0;  # @ x=a edge;
bc3 := w(x,0) = 0; # @ y=0 edge;
bc4 := w(x,b) = 0; # @ y=b edge;
bcx1 := -D11*D[2](w)(0,y) - D12*D[2](w)(0,y) = 0; # @ x=0 edge;
bcx2 := -D11*D[2](w)(a,y) - D12*D[2](w)(a,y) = 0; # @ x=a edge;
bcy1 := -D12*D[2](w)(x,0) - D22*D[2](w)(x,0) = 0; # @ y=0 edge;
bcy2 := -D12*D[2](w)(x,b) - D22*D[2](w)(x,b) = 0; # @ y=b edge;

sol := [myPDE1, bc1, bc2, bc3, bc4, bcx1, bcx2, bcy1, bcy2];

pdsolve(sol);

"Note:
and D11, D12, D22, D66 and G are constant.
The intention is to find the critical value for G"

I need help with how I can handle the boundary conditions for the problem. Thanks a million.

Hello everybody!
I have a PDE with initial and boundary conditions. I want to plot its solution by taking "t" as x axis. I have seen the documentation. It only has the space variable on x axis. Please show me a way to achieve what I intend.

here is the file pdsolve.mw

The value of x can be chosen as 0.16 or 0.21

I am trying to solve a PDE using pdsolve-numeric. I am getting an error related to boundary conditions.
Please see the follwing worksheet and suggest me some solutions

pdsolve.mw

Please help me.I don't know how to achieve the following iteration relation by maple code.iterative relationship

 

 

hi .may every one help me for pdsolve this differential equations?

all initial boundary condition are zero

thanks...

pdeSol_(1).mw

 

#
# Define some parameters
#
  sigma := 10; N := 0; beta := 1; alpha := 1; PDE1 := diff(w(X, theta, t), X, X, X, X)+2*alpha^2*(diff(w(X, theta, t), theta, theta, X, X))+alpha^4*(diff(w(X, theta, t), theta, theta, theta, theta))-N*(diff(w(X, theta, t), X, X))+diff(w(X, theta, t), t, t)-beta*w(X, theta, t)-sigma = 0

10

 

0

 

1

 

1

 

diff(diff(diff(diff(w(X, theta, t), X), X), X), X)+2*(diff(diff(diff(diff(w(X, theta, t), X), X), theta), theta))+diff(diff(diff(diff(w(X, theta, t), theta), theta), theta), theta)-10+diff(diff(w(X, theta, t), t), t)-w(X, theta, t) = 0

(1)

#
# Define the PDES
#
  PDEs:= { diff(w(X, theta, t), X, X, X, X)+2*alpha^2*(diff(w(X, theta, t), theta, theta, X, X))+alpha^4*(diff(w(X, theta, t), theta, theta, theta, theta))-N*(diff(w(X, theta, t), X, X))+diff(w(X, theta, t), t, t)-beta*w(X, theta, t)-sigma = 0
   };

{diff(diff(diff(diff(w(X, theta, t), X), X), X), X)+2*(diff(diff(diff(diff(w(X, theta, t), X), X), theta), theta))+diff(diff(diff(diff(w(X, theta, t), theta), theta), theta), theta)-10+diff(diff(w(X, theta, t), t), t)-w(X, theta, t) = 0}

(2)

#
# Set of boundary conditions at x=1.
#
   bcs1:= { D[1](w)(1,theta, t) = 0,
              w(1,theta, t) = 0
         };

{w(1, theta, t) = 0, (D[1](w))(1, theta, t) = 0}

(3)

#
# Set of boundary conditions at x=0
#
  bcs2:= {    w(0,theta, t)=0,
           D[1](w)(0,theta, t)=0
         };

{w(0, theta, t) = 0, (D[1](w))(0, theta, t) = 0}

(4)

#
# Set of boundary conditions at t=0
#
  bcs3:= { w(x,theta,0)=0,
          
           D[2](w)(x,theta,0)=0 };
           

{w(x, theta, 0) = 0, (D[2](w))(x, theta, 0) = 0}

(5)

 


  pdsolve( PDEs, `union`(bcs1, bcs2, bcs3), numeric);

Error, (in pdsolve/numeric/process_PDEs) can only numerically solve PDE with two independent variables, got {X, t, theta}

 

 

 

Download pdeSol_(1).mw

Hy Prof.

Please help me or guide me to get idea to solve Nonlinear coupled PDEwith MAPLE.Dr.Sam Dao could please help me as I saw your YOUTUBE lecturer which very helpful to me and please give some idea about my topic.

pde[1] := diff(u(x, t), t)-D(diff(u(x, t), x, x)) = alpha*u(x, t)*(1-v(x, t))

pde[2] := diff(v(x, t), t)-E(diff(v(x, t), x, x)) = beta*v(x, t)*(1-u(x, t))

Thanks in advance and answer is highly appricaited 

i have 2 PDE equations with some boundary conditions,maple get me errors, what should i do ? please help
how can i make correction in my system or boundary to have a solution ?

Download pde2.mw

tnx in advance

Can some one help me for converting three or two coupled pdes to odes using Lie group or any other method in maple

 

 

                                                                      

                                                                   

                                                                     

                                                                        

                                                                      

 

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?

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.

 

 

 

Hi all,

 

Please help me with this question. I want to solve a PDE by Maple.

restart

A := 5;

5

(1)

B := 9

9

(2)

c := 1

1

(3)

``

``

``

eq := diff(u(x, t), t, t)-c^2*(diff(u(x, t), x, x));

diff(diff(u(x, t), t), t)-(diff(diff(u(x, t), x), x))

(4)

 

dsolve({eq, u(0, t) = A, u(1, t) = B, u(x, 0) = 0, (D(u))(x, 0) = sin(x)}, u(x, t))

Error, (in evalapply/D) too many variables for the derivative of a function of only one variable in D(u)(x, 0)

 

``

``

``

 

Download SolvePDE.mwSolvePDE.mw

hi .please help me for solve this equations.

bbb2.mw

restart; d[11] := 1; mu[11] := 1; q[311] := 1; d[33] := 1; mu[33] := 1; a[11] := 1; e[311] := 1; a[33] := 1; A := 1; g[111111] := 1; c[1111] := 1; g[113113] := 1; f[3113] := 1; beta[11] := 1; `ΔT` := 1; II := 1; L := 1

J := d[11]*(diff(Phi(x, z), x, x))+mu[11]*(diff(psi(x, z), x, x))+q[311]*(diff(w(x), x, x))+d[33]*(diff(Phi(x, z), z, z))+mu[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(1)

B := a[11]*(diff(Phi(x, z), x, x))+d[11]*(diff(psi(x, z), x, x))+e[311]*(diff(w(x), x, x))+a[33]*(diff(Phi(x, z), z, z))+d[33]*(diff(psi(x, z), z, z));

diff(diff(Phi(x, z), x), x)+diff(diff(psi(x, z), x), x)+diff(diff(w(x), x), x)+diff(diff(Phi(x, z), z), z)+diff(diff(psi(x, z), z), z)

(2)

R := A*(g[111111]*(diff(u[0](x), x, x, x, x))-c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)));

diff(diff(diff(diff(u[0](x), x), x), x), x)-(diff(diff(u[0](x), x), x))-(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z)

(3)

S := -II*g[111111]*(diff(w(x), x, x, x, x, x, x))-II*c[1111]*(diff(w(x), x, x, x, x))+A*g[113113]*(diff(w(x), x, x, x, x))-A*f[3113]*(diff(diff(Phi(x, z), z), x, x))-A*(c[1111]*(diff(u[0](x), x, x)+(1/2)*(diff((diff(w(x), x))^2, x)))+e[311]*(diff(diff(Phi(x, z), z), x))+q[311]*(diff(diff(psi(x, z), z), x)))*(diff(w(x), x))-A*(diff(w(x), x, x))*(c[1111]*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2)+e[311]*(diff(Phi(x, z), z))+q[311]*(diff(psi(x, z), z))-beta[11]*`ΔT`);

-(diff(diff(diff(diff(diff(diff(w(x), x), x), x), x), x), x))-(diff(diff(diff(Phi(x, z), x), x), z))-(diff(diff(u[0](x), x), x)+(diff(w(x), x))*(diff(diff(w(x), x), x))+diff(diff(Phi(x, z), x), z)+diff(diff(psi(x, z), x), z))*(diff(w(x), x))-(diff(diff(w(x), x), x))*(diff(u[0](x), x)+(1/2)*(diff(w(x), x))^2+diff(Phi(x, z), z)+diff(psi(x, z), z)-1)

(4)

dsys := {B, J, R, S}; BCS := {D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

{D@@2*w(0) = 0, D@@2*w(L) = 0, Phi(x = 0) = 0, Phi(x = L) = 0, Phi(z = -(1/2)*h) = 0, Phi(z = (1/2)*h) = 0, psi(x = 0) = 0, psi(x = L) = 0, psi(z = -(1/2)*h) = 0, psi(z = (1/2)*h) = 0, w(x = 0) = 0, w(x = L) = 0, u[0](x = 0) = 0, u[0](x = L) = 0, (D(w))(0) = 0, (D(w))(L) = 0, (D(u[0]))(0) = 0, (D(u[0]))(L) = 0}

(5)

dsol5 := dsolve(dsys, numeric)

Error, (in dsolve/numeric/process_input) missing differential equations and initial or boundary conditions in the first argument: dsys

 

NULL

NULL

NULL

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

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?

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