Numerical solution of nonlinear ordinary differential equation for a turning point problem
type: Item
instance of: scholarly article
title: Numerical solution of nonlinear ordinary differential equation for a turning point problem
zbMATH Open document ID: 0756.65108
DOI: 10.1007/BF02015689
author: Peng-cheng Lin
author: Qingyuan Bai
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1992-09-27T00:00:00Z
review text: The authors consider the nonlinear differential problem \(\varepsilon^ 2u''+xa(u)u'-b(x)u=f(x)\), \(0<x<1\), with homogeneous Dirichlet conditions at the boundary. Assuming \(a(u(x))\geq a_ 0>0\) and \(b(x)\geq b_ 0 > 0\) some useful estimations for the solution \(u\) and its derivatives are obtained. On this base the uniform convergence of an exponential fitted difference scheme is proved by usual techniques. The paper ends with an illustrating example.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 61707
zbMATH Keywords: turning point problem
zbMATH Keywords: singular perturbation
zbMATH Keywords: numerical example
zbMATH Keywords: uniform convergence
zbMATH Keywords: exponential fitted difference scheme
reviewed by: Eckehard Pfeifer
MaRDI profile type: Publication
Wikidata QID: Q115392995
cites work: The numerical solution for problems of turning point without resonance
cites work: A uniformly convergent difference scheme for a semilinear singular perturbation problem
cites work: \(L^ 1\) and \(L^{\infty}\) uniform convergence of a difference scheme for a semilinear singular perturbation problem
cites work: A Priori Estimates and Analysis of a Numerical Method for a Turning Point Problem
full work available at URL: https://doi.org/10.1007/bf02015689
OpenAlex ID: W2053225411
description: scientific article; zbMATH DE number 61707