Transition probability coefficients and the stability of finite difference schemes for the diffusion and Telegraphers' equations

A probabilistic approach has been used to analyse the stability of the various finite difference formulations for propagation of signals on a lossy transmission line. If the sign of certain transition probabilities is negative, then the algorithm is found to be unstable. We extend the concept to consider the effects of space and time discretizations on the signs of the coefficients in a probabilistic finite difference implementation of the Telegraphers' equation and draw parallels with the transmission line matrix (TLM) technique. Copyright © 2002 John Wiley & Sons, Ltd.