High-order finite difference schemes for the solution of second-order BVPs
type: Item
instance of: scholarly article
title: High-order finite difference schemes for the solution of second-order BVPs
zbMATH Open document ID: 1073.65061
author: Pierluigi Amodio
author: Ivonne Sgura
published in: Journal of Computational and Applied Mathematics
publication date: 2005-02-23T00:00:00Z
review text: The paper is (mainly) concerned with two-point Dirichlet boundary value problems (BVPs) for second-order ordinary differential equations. The authors propose higher-order generalizations of classical finite difference schemes for their numerical solution. For this purpose, more than just direct neighbours are incorporated into the approximating formulas. A simple linear problem serves for analyzing the condition of the resulting matrix. Two numerical examples illustrate the quality of the proposed methods. Finally, a short proposal refers to applications to elliptic boundary value problems.
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2137363
zbMATH Keywords: Finite difference schemes
zbMATH Keywords: Boundary value methods
zbMATH Keywords: Two-point boundary value problems
zbMATH Keywords: conditioning analysis
zbMATH Keywords: numerical examples
reviewed by: Michael Plum
describes a project that uses: MIRKDC
describes a project that uses: bvp4c
MaRDI profile type: Publication
full work available at URL: j.cam.2004.07.008
OpenAlex ID: W2062911938
cites work: On the A-stable methods in the GBDF class
cites work: The conditioning of Toeplitz band matrices
cites work: Q4868576
cites work: Q4393432
cites work: A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
cites work: Runge–Kutta Software with Defect Control for Boundary Value ODE<scp>s</scp>
cites work: Spatial Finite Difference Approximations for Wave-Type Equations
cites work: Q4039971
cites work: Q4875410
cites work: Preconditioning and conditioning of systems arising form boundary value methods
cites work: Numerical approximation of nonlinear BVPs by means of BVMs
cites work: Numerical methods for second order singular perturbation problems
cites work: Q4303980
cites work: \(O(\tau^ 2 + h^ 4)\) finite difference scheme for decoupled system of two quasilinear parabolic equations
Wikidata QID: Q62027885
DOI: 10.1016/J.CAM.2004.07.008
description: scientific article; zbMATH DE number 2137363