A class of simple exponential B-splines and their application to numerical solution to singular perturbation problems
type: Item
instance of: scholarly article
title: A class of simple exponential B-splines and their application to numerical solution to singular perturbation problems
zbMATH Open document ID: 0676.65088
DOI: 10.1007/BF01398912
author: Manabu Sakai
author: Riaz A. Usmani
published in: Numerische Mathematik
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/133367
review text: The authors consider an application of simple exponential splines to the numerical solution of singular perturbation problem: \(\epsilon y''+b(x)y'-d(x)y=f(x),\) (0\(\leq x\leq 1)\), \(y(0)=\alpha\), \(y(1)=\beta\). More specifically, they propose a numerical scheme of collocation type using fourth order exponential splines. After giving the convergence theorem of order two for the numerical solution, they show two numerical examples to exhibit the less computational effort of their method than those of other methods of exponential type.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 4108077
zbMATH Keywords: exponential splines
zbMATH Keywords: singular perturbation
zbMATH Keywords: collocation type
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
zbMATH Keywords: methods of exponential type
reviewed by: Taketomo Mitsui
MaRDI profile type: Publication
cites work: Difference approximations for singular perturbations of systems of ordinary differential equations
cites work: An Analysis of a Uniformly Accurate Difference Method for a Singular Perturbation Problem
cites work: Analysis of Some Difference Approximations for a Singular Perturbation Problem Without Turning Points
cites work: A simple rational spline and its application to monotonic interpolation to monotonic data
description: scientific article; zbMATH DE number 4108077