Second-order accurate difference method for the singularly perturbed problem of fourth-order ordinary differential equations
type: Item
instance of: scholarly article
title: Second-order accurate difference method for the singularly perturbed problem of fourth-order ordinary differential equations
zbMATH Open document ID: 0753.65070
DOI: 10.1007/BF02016376
author: Guoying Wang
author: Minglun Chen
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1992-09-27T00:00:00Z
review text: For a class of boundary value problems for ordinary differential equations which are widely applied in mechanics: \(\varepsilon u^{(4)}- (a(x)u)''=f(x)\), \(0<x<1\), \(u(0)=u(1)=0\), \(u''(0)=u''(1)=0\), a uniform second-order difference scheme based on the use of the Petrov-Galerkin finite element method is constructed. A numerical example is given.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L60
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34E15
zbMATH DE Number: 60168
zbMATH Keywords: fourth order equation
zbMATH Keywords: singular perturbations
zbMATH Keywords: uniform second-order difference scheme
zbMATH Keywords: Petrov-Galerkin finite element method
zbMATH Keywords: numerical example
reviewed by: Pavol Chocholatý
MaRDI profile type: Publication
cites work: Q3909948
cites work: A Uniformly Accurate Finite Element Method for a Singular Perturbation Problem in Conservative Form
cites work: An Analysis of a Superconvergence Result for a Singularly Perturbed Boundary Value Problem
description: scientific article; zbMATH DE number 60168