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Nonstandard finite difference schemes for reaction--diffusion equations having linear advection

✍ Scribed by Ronald E. Mickens

Publisher: John Wiley and Sons
Year: 2000
Tongue: English
Weight: 48 KB
Volume: 16
Category: Article
ISSN: 0749-159X
DOI: 10.1002/1098-2426(200007)16:4<361::aid-num1>3.0.co;2-c

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✦ Synopsis

We extend previous work on nonstandard finite difference schemes for one-space dimension, nonlinear reaction-diffusion PDEs to the case where linear advection is included. The use of a positivity condition allows the determination of a functional relation between the time and space step-sizes, and provides schemes that are explicit. The Fisher equation is used to illustrate the method.

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