I wrote a short tutorial a while ago: http://fvt.simulkade.com/posts/2015-09-28-coupled-nonlinear-pdes-two-phase-flow-in-porous-media.html

And another tutorial for a single nonlinear PDE, with more details: http://fvt.simulkade.com/posts/2015-04-06-solving-nonlinear-pdes-with-fvm.html

I linearize the PDE and solve it in a finite volume tool I have written in Matlab: http://www.mathworks.com/matlabcentral/fileexchange/46637-a-simple-finite-volume-solver-for-matlab

Dear Meguenni, the term "Nonlinear PDE system" is too vague. Different types of PDEs require different techniques, and toolboxes may exist only for some specific class of equations/systems.

Moreover, to my knowledge, symbolic manipulators like Mathematica or Maple are unsuitable for PDE problems, which in general have no closed-form solution. You should better look for Matlab tollboxes.

@Roberto, Thank you for your reply, I am trying to solve a system of equations by a finite difference method. the concern is this, the result of descretisation brings me back to a equations nonlinear system. this is new to me, because usually I use Gauss-Seidel algorithm for solving this kind of problem, but it is only valid for linear systems.

Other things, the stability and accuracy of the solution, I do not have enough time to see a range of theories (I must do work quickly enough).

that's why I like to have a tutorial that summarizes everything.

Dear Meguenni Bouhadjar,

have a look at the attached document and let me know if you need help on any other method.

Regards,

Anees Ahmed Awan

@Anees, Thank you, but the attached document is about the Newton's Method.

Regards.

which method do you need?

I wrote a short tutorial a while ago: http://fvt.simulkade.com/posts/2015-09-28-coupled-nonlinear-pdes-two-phase-flow-in-porous-media.html

And another tutorial for a single nonlinear PDE, with more details: http://fvt.simulkade.com/posts/2015-04-06-solving-nonlinear-pdes-with-fvm.html

I linearize the PDE and solve it in a finite volume tool I have written in Matlab: http://www.mathworks.com/matlabcentral/fileexchange/46637-a-simple-finite-volume-solver-for-matlab