Numerical solution of a non-linear system of partial differential equations

I need:
1. Numerical solution of system of non linear coupled partial differential equations by two methods.
2. Visual representation of the numerical results against various parameters.
3. The detail matlab code of both methods.
4. Detail report of both methods.
5. The comparison of the numerical solutions obtained from the two different numerical scheme.
6. The method reports must b such that one can easily understand the method and help to understand the code in matlab.
7. Comment code in detail.