Nonstandard finite difference method by nonlocal approximation
type: Item
instance of: scholarly article
title: Nonstandard finite difference method by nonlocal approximation
zbMATH Open document ID: 1015.65034
DOI: 10.1016/S0378-4754(02)00106-4
author: Roumen Anguelov
author: Jean Lubuma
published in: Mathematics and Computers in Simulation
publication date: 2003-03-16T00:00:00Z
review text: Two types of monotonic properties of solutions of differential equations are discussed and general finite difference schemes, which are stable with respect to these properties are investigated. Apart from being elementary stable, these schemes are also shown to preserve qualitative properties of nonhyperbolic fixed points of the differential equations. From the practical point of view, a systematic procedure based on nonlocal approximation is proposed for the construction of qualitatively stable nonstandard finite difference schemes for the logistic equation, the combustion model and the reaction-diffusion equation.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 80A25
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35L65
zbMATH DE Number: 1882284
zbMATH Keywords: nonstandard finite difference method
zbMATH Keywords: nonlocal approximation
zbMATH Keywords: qualitatively stable nonstandard finite difference schemes
zbMATH Keywords: logistic equation
zbMATH Keywords: combustion model
zbMATH Keywords: reaction-diffusion equation
reviewed by: Leonid B. Chubarov
MaRDI profile type: Publication
cites work: Q4524879
cites work: Contributions to the mathematics of the nonstandard finite difference method and applications
cites work: Nonstandard methods for advection-diffusion-reaction equations
cites work: Q4002473
cites work: Q4309510
cites work: Nonstandard finite difference schemes
cites work: Q5536978
cites work: Q3838091
full work available at URL: s0378-4754(02)00106-4
OpenAlex ID: W2029844829
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description: scientific article; zbMATH DE number 1882284