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Transition probability coefficients and the stability of finite difference schemes for the diffusion and telegraphers’ equations. (English) Zbl 0996.65097

Summary: 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. 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 technique.

MSC:

65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35L05 Wave equation
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References:

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