Process Dynamics: Explicit Vs. Crank-Nicolson Method

We are deriving the time-dependent heat diffusion equation for a uniform linear bar, assuming constant thermal diffusivity. Then, use the heat diffusion equation as an algebraic equation via explicit and Crank-Nicolson differencing. With Von Neumann stability analysis, we can explain why the simulation results would be unstable when r is set larger than 0.5 for explicit. As well as showing the stability analysis with Crank-Nicolson.