Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
type: Item
instance of: scholarly article
title: Nonstandard finite difference equations for ODEs and 1-D PDEs based on piecewise linearization
zbMATH Open document ID: 0907.65075
DOI: 10.1016/S0096-3003(96)00146-4
author: C. M. García-López
author: Juan I. Ramos
published in: Applied Mathematics and Computation
publication date: 1999-03-04T00:00:00Z
review text: The authors construct nonstandard finite difference schemes for nonlinear ordinary and one-dimensional partial differential equations. The method of construction consists in employing piecewise linearization, which reduces the nonlinear equation to a piecewise one. The latter can be integrated analytically subject to appropriate continuity conditions for both its solution and the first-order derivative of the solution in order to get three-point nonlinear difference schemes, the solution of which provides the nodal values of the approximate solution. The solution of the nonlinear difference schemes requires the use of iterative techniques.
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 35K55
zbMATH DE Number: 1183156
zbMATH Keywords: nonstandard finite difference schemes
zbMATH Keywords: piecewise linearization
reviewed by: Vladimir L. Makarov
MaRDI profile type: Publication
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cites work: Adaptive methods of lines for one‐dimensional reaction‐diffusion equations
cites work: Q4077008
cites work: Q4040640
cites work: Q3662554
cites work: A PIECEWISE-LINEARIZED METHOD FOR ORDINARY DIFFERENTIAL EQUATIONS: TWO-POINT BOUNDARY-VALUE PROBLEMS
cites work: Piecewise-linearized methods for initial-value problems
cites work: Numerical Inversion of Laplace Transforms: An Efficient Improvement to Dubner and Abate's Method
cites work: Transient analysis by Laplace transform and combined finite and boundary element methods for convective diffusion problem
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cites work: Numerical study of Fisher's equation by Adomian's method
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cites work: Multiple scale and singular perturbation methods
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cites work: A computational method for solving quasilinear singular perturbation problems
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cites work: Asymptotic and numerical analysis of singular perturbation problems: A survey
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cites work: Finite-element methods for singularly perturbed high-order elliptic two-point boundary value problems. I: reaction-diffusion-type problems
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cites work: RELAXATION METHODS APPLIED TO DETERMINE THE MOTION, IN TWO DIMENSIONS, OF A VISCOUS FLUID PAST A FIXED CYLINDER
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cites work: Ten ways to generate the Il'in and related schemes
full work available at URL: s0096-3003(96)00146-4
OpenAlex ID: W2170349946
description: scientific article; zbMATH DE number 1183156