Reverse boundary conditions in a one-dimensional degenerate PDE

I want to solve a PDE with convection and diffusion, which has travelling waves solutions which go from 1 to 0 and travel from left to right as the picture attached. It happens that this equation also has the same solutions but travelling from right to left and going from 0 to 1 (like the attached picture, the last profile from right to left is the first one).

To obtain the normal (left to right) profiles the initial conditions could be for example a step function or a tanh. The boundary conditions are u(xl,t)=1 and u(xr,t)=0. This is how I code this:

function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t) pl = ul; ql = 0; pr = ur; qr = 0;

If I want to obtain the right to left profiles, strictly speaking I only need to "reverse" the boundary and initial conditions appropriately. That is, for example a –tanh (instead of +) and something like: u(xl,t)=0 and u(xr,t)=1. This is how I changed it:

function [pl,ql,pr,qr] = pdex1bc(xl,ul,xr,ur,t) pl = ur; ql = 0; pr = ul; qr = 0;

However this does not work, i get the following error:

Error using pdepe (line 293) Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.

Error in test4 (line 50) sol = pdepe(m,@pdex1pde,@pdex1ic1,@pdex1bc,x,t);

which is weird because the normal case works fine (that is the normal case already had convection and density dependent diffusion), I think that I am not putting the BC properly.

I must add that I have been able to show that these type of waves are solutions using another numerical software (and by changing the initial and boundary conditions is how I obtained it). So it’s just a matter of coding the initial conditions properly I think.

If you have guys have any advise I will appreciate it vey much.

I am using Matlab_R2014a and the PDE solver is pdepe. I can send you my code if needed. Many thanks in advance.

[Torsten]

Yes, it would be helpful if you include the code for the case where pdepe fails.

Best wishes

Torsten.