A fourth-order finite difference method for the general one-dimensional nonlinear biharmonic problems of first kind
type: Item
instance of: scholarly article
title: A fourth-order finite difference method for the general one-dimensional nonlinear biharmonic problems of first kind
zbMATH Open document ID: 0963.65083
DOI: 10.1016/S0377-0427(99)00202-2
published in: Journal of Computational and Applied Mathematics
publication date: 2000-03-21T00:00:00Z
review text: This paper derives a fourth-order difference scheme for fourth-order boundary value problems subject to natural boundary conditions based on only three grid points. The ensuring coupled block systems can be solved iteratively by block successive overrelaxation (either linearly or nonlinearly depending on the differential equation). Convergence properties of these iterations are studied analytically for a model linear problem and numerical results are presented. There are issues associated with convergence and loss of order due to roundoff errors.
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1419821
zbMATH Keywords: nonlinear biharmonic problems
zbMATH Keywords: numerical examples
zbMATH Keywords: convergence
zbMATH Keywords: fourth-order difference scheme
zbMATH Keywords: fourth-order boundary value problems
zbMATH Keywords: successive overrelaxation
zbMATH Keywords: roundoff errors
author: R. K. Mohanty
reviewed by: Kevin Burrage
MaRDI profile type: Publication
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Wikidata QID: Q127865167
description: scientific article; zbMATH DE number 1419821