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A best finite‐difference scheme for the fisher equation
Author(s) -
Mickens Ronald E.
Publication year - 1994
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/num.1690100505
Subject(s) - mathematics , partial differential equation , finite difference , fisher equation , differential equation , class (philosophy) , finite difference method , first order partial differential equation , scheme (mathematics) , fisher's equation , finite difference scheme , finite difference coefficient , mathematical analysis , exact differential equation , finite element method , mixed finite element method , computer science , physics , real interest rate , artificial intelligence , monetary economics , economics , thermodynamics , interest rate
A new class of finite‐difference schemes is constructed for the Fisher partial differential equation. These schemes are constructed according to the nonstandard modeling rules formulated by Mickens. They have the property that, in the appropriate limits, the discrete models obtained are either “exact” or “best” finite‐difference schemes for corresponding differential equation. Consequently, the elementary numerical instabilities will not occur. © 1994 John Wiley & Sons, Inc.