A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation

This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmission‐line modelling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit Crank–Nicolson routine may be expressed as the exact solution of certain transmission‐line models. Using these models a technique for comparing the accuracy and stability of numerical routines is developed and a detailed comparison of the new TLM methods and the well established methods is made.