High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems
type: Item
instance of: scholarly article
title: High order parameter-robust numerical method for singularly perturbed reaction-diffusion problems
zbMATH Open document ID: 1229.65129
author: Mukesh Kumar
author: S. Chandra Sekhara Rao
published in: Applied Mathematics and Computation
publication date: 2010-05-25T00:00:00Z
review text: This paper presents a higher-order parameter-uniform numerical method for singularly perturbed one-dimensional linear self-adjoint two-point boundary-value problems. The numerical scheme combines both the fourth-order compact difference scheme and the classical central difference scheme on generalized piecewise-uniform Shishkin meshes. Error estimates are derived and numerical examples are presented.
reviewed by: Srinivasan Natesan
Mathematics Subject Classification ID: 65L11
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L70
zbMATH DE Number: 5711768
zbMATH Keywords: singular perturbation
zbMATH Keywords: hybrid scheme
zbMATH Keywords: generalized Shishkin mesh
zbMATH Keywords: parameter-robust convergence
zbMATH Keywords: global error estimate
zbMATH Keywords: reaction-diffusion problems
zbMATH Keywords: pointwise error estimate
zbMATH Keywords: linear self-adjoint two-point boundary-value problems
zbMATH Keywords: fourth-order compact difference scheme
zbMATH Keywords: central difference scheme
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: j.amc.2010.01.121
OpenAlex ID: W2042719590
cites work: Q5610080
cites work: High order methods for elliptic and time dependent reaction-diffusion singularly perturbed problems
cites work: Q3909948
cites work: Q4485828
cites work: Q2724516
cites work: On a fourth-order finite-difference method for singularly perturbed boundary value problems
cites work: A survey of numerical techniques for solving singularly perturbed ordinary differential equations
cites work: Robust convergence of a compact fourth-order finite difference scheme for reaction-diffusion problems
cites work: Q4486278
cites work: A Uniformly Accurate Finite-Element Method for a Singularly Perturbed One-Dimensional Reaction-Diffusion Problem
cites work: High order fitted operator numerical method for self-adjoint singular perturbation problems
cites work: High order parameter uniform numerical method for singular perturbation problems
cites work: Q4871736
cites work: Q3813229
cites work: Q5342712
cites work: A higher-order scheme for quasilinear boundary value problems with two small parameters
cites work: A priori meshes for singularly perturbed quasilinear two-point boundary value problems
cites work: Q4378275
DOI: 10.1016/J.AMC.2010.01.121
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description: scientific article; zbMATH DE number 5711768