Numerical treatment of singularly perturbed two point boundary value problems using initial-value method
type: Item
instance of: scholarly article
title: Numerical treatment of singularly perturbed two point boundary value problems using initial-value method
zbMATH Open document ID: 1177.65109
author: J. Blot
published in: Journal of Applied Mathematics and Computing
publication date: 2009-10-26T00:00:00Z
review text: The authors describe an initial-value method for linear and nonlinear singularly perturbed boundary value problems in the interval \([p,q]\). For linear problems, the required approximate solution is obtained by solving the reduced problem and one initial-value problem directly deduced from the given problem. For non-linear problems the original second-order nonlinear problem is linearized by using quasilinearization method. The resulting linear problem is solved by the previous method. The present method is implemented on several linear and non-linear examples which approximate the exact solution. The authors also present the approximate and exact solutions graphically.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 5620575
zbMATH Keywords: singular perturbation
zbMATH Keywords: boundary layers
zbMATH Keywords: initial-value method
zbMATH Keywords: quasilinearization
zbMATH Keywords: numerical examples
reviewed by: G. Vanden Berghe
MaRDI profile type: Publication
full work available at URL: s12190-008-0127-3
OpenAlex ID: W2023482430
cites work: Collocation for Singular Perturbation Problems I: First Order Systems with Constant Coefficients
cites work: Collocation for Singular Perturbation Problems II: Linear First Order Systems Without Turning Points
cites work: Collocation for Singular Perturbation Problems III: Nonlinear Problems without Turning Points
cites work: Q3207312
cites work: Collocation with Polynomial and Tension Splines for Singularly-Perturbed Boundary Value Problems
cites work: Q3862348
cites work: Singular perturbations and differential inequalities
cites work: Initial-value technique for a class of nonlinear singular perturbation problems
cites work: Perturbation methods in applied mathematics
cites work: Numerical Methods for Singular Perturbation Problems
cites work: An Initial-Value Technique for Singularly Perturbed Boundary Value Problems via Cubic Spline
cites work: The nonlinear singularly perturbed initial boundary value problems of nonlocal reaction diffusion systems
cites work: Initial-value technique for singularly-perturbed turning-point problems exhibiting twin boundary layers
cites work: ``Shooting method'' for the solution of singularly perturbed two-point boundary-value problems having less severe boundary layer.
cites work: A boundary value technique for singular perturbation problems
cites work: A second order monotone upwind scheme
cites work: Techniques of asymptotic analysis
cites work: A Uniformly Accurate Finite Element Method for a Singular Perturbation Problem in Conservative Form
cites work: Adaptivity and Error Estimation for the Finite Element Method Applied to Convection Diffusion Problems
cites work: An efficient numerical method for singular perturbation problems
DOI: 10.1007/S12190-008-0127-3
description: scientific article; zbMATH DE number 5620575