Variable mesh spline approximation method for solving singularly perturbed turning point problems having boundary layer(s)
type: Item
instance of: scholarly article
title: Variable mesh spline approximation method for solving singularly perturbed turning point problems having boundary layer(s)
zbMATH Open document ID: 1003.65085
DOI: 10.1016/S0898-1221(01)00253-X
publication date: 2002-08-25T00:00:00Z
review text: The authors consider linear second-order ordinary differential equations where the coefficient of the second-order derivative is small and the boundary values are known and suggest an approximate solution by means of cubic splines. They discuss strategies for generating a mesh according to whether these are one or two boundary layer regions and consider the convergence criteria. Numerical results are given for some particular examples for a varying number of points in the boundary layer and there is a discussion of the results obtained.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 1787776
zbMATH Keywords: variable mesh spline approximation
zbMATH Keywords: turning point
zbMATH Keywords: boundary layer
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical examples
zbMATH Keywords: mesh generation
zbMATH Keywords: linear second-order ordinary differential equations
zbMATH Keywords: cubic splines
zbMATH Keywords: convergence
author: M. K. Kadalbajoo
author: Kailash C. Patidar
reviewed by: Ll. G. Chambers
MaRDI profile type: Publication
cites work: A Priori Estimates for Solutions of Singular Perturbations with a Turning Point
cites work: A Priori Estimates and Analysis of a Numerical Method for a Turning Point Problem
cites work: Continuous and Numerical Analysis of a Multiple Boundary Turning Point Problem
cites work: Q3923536
cites work: Sufficient Conditions for the Uniform Convergence of a Difference Scheme for a Singularly Perturbed Turning Point Problem
cites work: Finite element methods on piecewise equidistant meshes for interior turning point problems
cites work: Q4211466
cites work: Q4316739
cites work: Numerical Methods for Singular Perturbation Problems
cites work: Semianalytic Numerical Studies of Turning Points Arising in Stiff Boundary Value Problems
cites work: On a Differential Equation of Boundary Layer Type
cites work: Q5540873
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: An Analysis of a Uniformly Accurate Difference Method for a Singular Perturbation Problem
cites work: Matched asymptotic expansions. Ideas and techniques
cites work: Q3862348
cites work: Q3909948
cites work: Q4486278
cites work: Q5533735
full work available at URL: s0898-1221(01)00253-x
OpenAlex ID: W2016632222
Wikidata QID: Q126788929
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1787776