Finite Difference Method in Matlab

I have the below set of equations and boundary conditions governing two phase fluid flow in an oil well and am struggling to start with a code to solve these with the finite difference method. I am looking to solve for Sw as function of radial distance r.

The variables are Po, Pw, So, Sw, r & t. The rest are constants which I have expertimetnal values for.

Any help would be highly appreciated as to how to start solving.

Thanks

[Torsten]

Very, very difficult to solve.

You should use commercial software or at least a free solver that is especially written for this type of equations.

Here is the preferred software for your application:

https://www.cmgl.ca/stars