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Please help to understand why NDSolve is not solving a nonlinear PDE in 2D?

Hello, I am solving the Belousov-Zhabotinsky system of PDE following the Gray-Scott scheme. When only the dynamical system is requested to be solved, NDSolve is giving the solution right away, however; when the diffusion term is added in 2D with Newman conditions at the boundaries (rectangular region), I tried different options and no one works. It seems to me that the numerical aspects of the problems (options for methods) are the key. What I expect to see? either concentric waves or spirals or maze-like patterns.

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POSTED BY: David Quesada
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Ok. So the error message was helpful in finding the error in the pde's. Concerning the numerical problems I learned in former times, that sometimes a rescaling of the variables (concentration, time and lengths), so that constants have about the same order of magnitude, turns out to make things running smoothly. But I can't make a proposal having not looked intensely at your system.

Regards Hans

POSTED BY: Hans Dolhaine

Hi Hans: I found in the definition of the Laplacian in the second equation the index for the variable C it was C1 when it should be C2, cause the message of derivative of higher order. Second, I changed the way I wrote the Newmann boundary conditions at the frontier points. I fixed all of these and it is running now, however giving some errors of stiffness and that I should run with MinStepSize lower in order to capture the rapid variations. I did MinStepSize -> 0.005, takes a while for computing, it is not giving me yet what I am suppose to see, because the numerical error still persist, negative values for the concentration for example and exponential explosion of the numerical values, that does not make any sense. On the positive side, I have to say that the nonlinearity concern due to one of the functions is dissipating a bit.

POSTED BY: David Quesada

No, I don't think that the non-linearity has something to do with the error.

And that is really mystic. I reduced the problem to one dimension AND removed the derivative of C2 in the boundary condition, but nevertheless the error message persists ???????

Look at the notebook.

Regards Hans

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POSTED BY: Hans Dolhaine
POSTED BY: David Quesada
POSTED BY: David Quesada
Attachments:
POSTED BY: Hans Dolhaine
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POSTED BY: David Quesada

Hello - the content of your notebook looks quite complicated. Could you give an abbreviated form which points out your problem?

Regards Hans

POSTED BY: Hans Dolhaine
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