Automated allocation of mesh points for stiff two-point boundary value problems
type: Item
instance of: scholarly article
title: Automated allocation of mesh points for stiff two-point boundary value problems
zbMATH Open document ID: 0744.65054
DOI: 10.1016/0898-1221(91)90071-B
author: Ram P. Manohar
author: Tat Y. Ngai
publication date: 1992-06-26T00:00:00Z
review text: The numerical solution of stiff two-point boundary value problems for a system of \(n\) differential equations (1) \(dy/dt=F(t,y)\), \(a<t<b\); \(B(y(a),y(b))=0\), where \(y^ T=(y_ 1,y_ 2,\dots,y_ n)\) is a given vector, is considered. A general procedure requiring negligible prerequisites to the problem is obtained to automate the allocation of mesh points by constructing a diffeomorphism \(t=\psi(u)\) from \([a,b]\) to \([a,b]\). It is the composition of the diffeomorphisms \(t=p(s)\), whose inverse is a solution of an initial value problem (2) \(ds/dt=Q(t,y)\), \(a<t<b\); \(s(a)=c\), where \(Q>0\) is a continuous ``density function'' to be constructed, and \(s=q(u)\) being a solution of the boundary value problem (3) \(d^ 2s/du^ 2=0\), \(a<b\); \(s(a)=c\), \(s(b)=d\). A properly constructed \(\psi\) smooths out the sharp corners in the solution while it leaves the domain boundary and the boundary conditions unchanged in the augmented and transformed system (1)-(3).
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L50
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 24507
zbMATH Keywords: automated allocation of mesh points
zbMATH Keywords: stiff two-point boundary value problems
zbMATH Keywords: diffeomorphisms
reviewed by: L. M. Berkovich
MaRDI profile type: Publication
cites work: Numerical Methods for Stiff Two-Point Boundary Value Problems
cites work: Graded-Mesh Difference Schemes for Singularly Perturbed Two-Point Boundary Value Problems
cites work: Singularly Perturbed Spline Difference Schemes on a Non‐Equidistant Grid
cites work: A uniform scheme for the singularly perturbed Riccati equation
cites work: Variable mesh methods for the numerical solution of two-point singular perturbation problems
full work available at URL: 0898-1221(91)90071-b
OpenAlex ID: W2018641930
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 24507