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General solutions of a three-level partial difference equation

✍ Scribed by Sui Sun Cheng; Yi-Feng Lu

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 655 KB
Volume: 38
Category: Article
ISSN: 0898-1221
DOI: 10.1016/s0898-1221(99)00239-4

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✦ Synopsis

This paper is concerned with a linear partial difference equation which includes the well-known DuFort Frankel multilevel difference scheme for the heat equation. By introducing Green's functions for this equation, we obtain, via a novel formal approach, an explicit formula for all its solutions. Given exponential initial conditions, separable solutions are also found. As applications, we derive several stability criteria for the solutions of this equation.

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