How to Solve a Nonlinear PDE System with Non-Diagonal 'c' Matrix in Matlab?

[Mingf]

I'm solving a nonlinear pde system in one space. It looks that the pdepe function won't work, because it only accepts coupled term in 's', not 'c' and 'f'. My equations are like:

\partial u1\partial t + c(u2)*\partial u2\partial t = f1(u2)*D^2 u1Dx^2 + s1(u1,u2);
\partial u2\partial t = f2*D^2 u2Dx^2 + s2(u1,u2);

So instead of a column vector for 'c', which is required in pdepe function description, I have a non-diagonal 'c' matrix.
Does anybody has any idea? Thanks!

 

[Aaron Bex]

If the problem is just two coupled equations, you can try using the ode45 or ode23s functions in MATLAB. These functions are designed for solving systems of ordinary differential equations. Alternatively, depending on the structure of your equations, you may be able to rewrite them as two separate nonlinear PDEs and use the pdepe function.

 

[oswaler]

I understand the frustration of encountering limitations in software tools when trying to solve complex problems. In this case, it seems that the pdepe function in Matlab is not able to handle your specific system of nonlinear PDEs due to the presence of a non-diagonal 'c' matrix.

One possible solution could be to look for alternative numerical methods that are capable of handling nonlinear PDE systems with non-diagonal coefficients. For example, you could explore the use of finite difference methods or spectral methods, which may offer more flexibility in terms of the types of equations they can handle.

Alternatively, you could try to reformulate your system of equations to make it compatible with the pdepe function. This may involve making approximations or simplifications, but it could potentially allow you to use the built-in capabilities of Matlab.

Ultimately, the best approach will depend on the specific details of your problem and the level of accuracy and efficiency required in your solution. I would recommend consulting with a numerical methods expert or seeking advice from the Matlab community to help find the most suitable solution for your specific case.