Hans Petter Langtangen coauthored a text on finite difference methods for partial differential equations with Svein Linge. Its treatment of diffusion equations derives discrete updates and investigates their stability. The connection between an explicit Euler method and a spatial second-difference operator makes the restriction on the time step visible in a reproducible computational model.[ref]
Finite Difference Computing with PDEs by Hans Petter Langtangen and Svein Linge. Chapter 3, Section 3.1
Articles by others on the same topic
GitHub account: github.com/hplgit
It should be mentioned that when you start Googling for PDE stuff, you will reach Han's writings a lot under his GitHub Pages: hplgit.github.io/, and he is one of the main authors of the FEniCS Project.
He also published to GitHub pages with his own crazy markdown-like multi-output markup language: github.com/hplgit/doconce.
Rest in peace, Hans.