PDEPE solver with off-diagonal coefficients

Hello,

referring to the pdex4 example, I am trying to understand if the function f in this part of the code:

function [c,f,s] = pdex4pde(x,t,u,DuDx)
c = [1; 1];
f = [0.024; 0.17] .* DuDx;
y = u(1) - u(2);
F = exp(5.73*y)-exp(-11.47*y);
s = [-F; F];

can be modified by substituting the vector [0.024; 0.17] with a 2x2 matrix.

Basically, I would need to solve a system like this:

%   |1|         |u1|      | d11*D(u1)/Dx + d12*D(u2)/Dx |   
%   | | .*  D_  |  | = D_ |                             | 
%   |1|     Dt  |u2|   Dx | d21*D(u1)/Dx + d22*D(u2)/Dx |
%
%   ---         ---             ------------------  
%    c           u                f(x,t,u,Du/Dx)       

Also, is the PDEPE solver the most appropriate for this problem?

Thanks in advance

MG

[Torsten]

As PDE equation, you can set this in "pdepe", but the problem will be the boundary condition function if derivatives of u1, u2 are involved.

[MG]

Ok, thank you for your reply.

At the moment, this is a secondary issue to consider, I am just wondering if the PDEPE is the correct solver and if it allows solving this kind of problem.

I am still thinking about the general problem and I am not sure that BCs will comprise the derivative of u. In case, what kind of limitation should I handle?

Thank you

[Torsten]

The boundary conditions have the general form

p + q*f = 0

where f in your example above is

f=[d11*DuDx(1)+d12*DuDx(2);d21*DuDx(1)+d22*DuDx(2)].

Thus you have to specify p(1),q(1), p(2), q(2) such that

p(1) + q(1)*(d11*DuDx(1)+d12*DuDx(2)) = 0
p(2) + q(2)*(d21*DuDx(1)+d22*DuDx(2)) = 0

Best wishes

Torsten.

[MG]

Of course, thank you, I am coding this part of the model just now.

Luckily for me, I don't need to add exotic functions in BCs, but only fixed coefficients.

Thank you for your kind support, cheers

MG