I have a decent familiarity with the numerical methods used for solving partial differential equations. A lot of it just involves discretizing the PDE and converting it into a linear system of equations. In the case of finite difference methods, this is pretty straight forward, in the case of spectral methods or finite elements this involves using a different basis, etc.
However, I tend to learn best when I can see a bunch of coded or programmed examples of a PDE and then the corresponding programming implementation of that numerical solution. As PDEs get more complicated, programming them gets more complicated as well. For example boundary conditions get more challenging, or there could be stiffness in the timestepping, etc. Many books provide the coded solution for say the heat equation and the Laplace equation, and then they stop giving the code. I was hoping to find a book with just a bunch of coded examples of PDE solutions. I would like to get up to some nonlinear reaction-diffusion equations if possible.
Does something like this exist? I the to work in Julia, but something in Matlab, or python, etc. or such would be fine. Just seeing how the discretization is managed would really help.