Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
type: Item
instance of: scholarly article
title: Numerical solution of a singularly perturbed two-point boundary value problem using equidistribution: Analysis of convergence
zbMATH Open document ID: 0977.65069
DOI: 10.1016/S0377-0427(99)00315-5
author: Yanyan Li
published in: Journal of Computational and Applied Mathematics
publication date: 2001-07-15T00:00:00Z
review text: This paper deals with the numerical approximation of the singularly perturbed boundary value problem (BVP) \[ -\varepsilon u_{xx}- p(x) u_x= 0,\quad x\in (0,1),\quad u(0)= 0,\quad u(1)= 1, \] where \(\varepsilon\) is a constant satisfying \(0<\varepsilon\leq 1\). An error analysis of upwind finite difference schemes for solving this BVP is presented on a grid that is constructed adaptively from the knowledge of the exact solution. The obtained discrete solutions are uniformly convergent with respect to \(\varepsilon\). The distribution of the error is shown for some numerical examples.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 1437657
zbMATH Keywords: singular perturbation
zbMATH Keywords: convergence
zbMATH Keywords: boundary value problem
zbMATH Keywords: error analysis
zbMATH Keywords: finite difference schemes
zbMATH Keywords: numerical examples
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
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full work available at URL: s0377-0427(99)00315-5
OpenAlex ID: W2055126073
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description: scientific article; zbMATH DE number 1437657