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 modeling (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.