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Transition probability coefficients and the stability of finite difference schemes for the diffusion and Telegraphers' equations
Author(s) -
Malachowski Michal J.
Publication year - 2002
Publication title -
international journal of numerical modelling: electronic networks, devices and fields
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.249
H-Index - 30
eISSN - 1099-1204
pISSN - 0894-3370
DOI - 10.1002/jnm.439
Subject(s) - probabilistic logic , stability (learning theory) , mathematics , finite difference , diffusion , stochastic matrix , lossy compression , finite difference method , sign (mathematics) , telegrapher's equations , space (punctuation) , matrix (chemical analysis) , mathematical analysis , transmission line , computer science , physics , statistics , materials science , telecommunications , machine learning , markov chain , composite material , thermodynamics , operating system
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.