A simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation
Abstract
This paper describes a simple explicit and unconditionally stable numerical routine for the solution of the diffusion equation using a transmissionline modeling (TLM) method. The paper also shows that the explicit finite difference routine and the implicit CrankNicolson routine may be expressed as the exact solution of certain transmissionline 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.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 1977
 DOI:
 10.1002/nme.1620110810
 Bibcode:
 1977IJNME..11.1307J
 Keywords:

 Diffusion Waves;
 Finite Difference Theory;
 Mathematical Models;
 Maxwell Equation;
 Numerical Stability;
 Transmission Lines;
 Analog Simulation;
 Approximation;
 Diffusion Theory;
 Electric Power Transmission;
 Error Analysis;
 Propagation Modes;
 Physics (General)