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Nonstandard finite difference schemes for reaction‐‐diffusion equations having linear advection
Author(s) -
Mickens Ronald E.
Publication year - 2000
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/1098-2426(200007)16:4<361::aid-num1>3.0.co;2-c
Subject(s) - mathematics , advection , partial differential equation , dimension (graph theory) , nonlinear system , finite difference , finite difference method , space (punctuation) , diffusion , mathematical analysis , fisher equation , partial derivative , work (physics) , pure mathematics , computer science , physics , real interest rate , quantum mechanics , monetary economics , economics , thermodynamics , interest rate , operating system
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. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 361–364, 2000