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Proceedings Paper

Stability of diffusion equation solution using various formulations of the finite difference method
Author(s): Michal Malachowski; Jadwiga Olesik
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Paper Abstract

A probabilistic approach has been used to analyze the stability of the various finite difference formulations for propagation of signals on a lossy transmission line. We extend the concept to consider the effects of space and time discretisations on the signs of the coefficients in a probabilistic finite difference implementation of the Telegraphers’ equation. We have found that if the sign of certain transition probabilities is negative then the algorithm is found to be unstable. The results of numerical analysis show that the following formulations of the diffusion and the Telegrapher’s equation gives the acceptable solutions: the backward difference, the central difference and Telegraphers’ equation with combination of central and backward differences. However the forward difference formulation of the diffusion equation gives the different results.

Paper Details

Date Published: 24 April 2003
PDF: 8 pages
Proc. SPIE 5116, Smart Sensors, Actuators, and MEMS, (24 April 2003);
Show Author Affiliations
Michal Malachowski, Pedagogical Univ. of Czestochowa (Poland)
Jadwiga Olesik, Pedagogical Univ. of Czestochowa (Poland)

Published in SPIE Proceedings Vol. 5116:
Smart Sensors, Actuators, and MEMS
Jung-Chih Chiao; Vijay K. Varadan; Carles Cané, Editor(s)

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