A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations
type: Item
instance of: scholarly article
title: A finite difference scheme for a class of singularly perturbed initial value problems for delay differential equations
zbMATH Open document ID: 1206.65191
author: Fevzi Erdogan
author: Gabil M. Amiraliyev
published in: Numerical Algorithms
publication date: 2010-01-04T00:00:00Z
review text: The authors consider a singularly perturbed initial value problem for a quasilinear first order delay differential equation, and construct a numerical method for this problem which involves an appropriate piecewise-uniform mesh on each time subinterval. They prove the first order convergence except for a logarithmic factor of this approximate solution in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical experiments.
reviewed by: Ziwen Jiang
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 34K26
Mathematics Subject Classification ID: 34K28
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 5652348
zbMATH Keywords: delay differential equation
zbMATH Keywords: singular perturbation
zbMATH Keywords: finite difference scheme
zbMATH Keywords: piecewise-uniform mesh
zbMATH Keywords: error estimates
zbMATH Keywords: initial value problem
zbMATH Keywords: quasilinear
zbMATH Keywords: first order
zbMATH Keywords: convergence
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s11075-009-9306-z
OpenAlex ID: W1964747200
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DOI: 10.1007/S11075-009-9306-Z
description: scientific article; zbMATH DE number 5652348