2003•Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIERequires access
Stability of diffusion equation solution using various formulation of finite difference method
Michał J. Małachowski, Jadwiga Olesik
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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.