A note on stability of a three-stage difference scheme for ordinary differential equations
type: Item
instance of: scholarly article
title: A note on stability of a three-stage difference scheme for ordinary differential equations
zbMATH Open document ID: 0770.65046
DOI: 10.1016/0898-1221(93)90209-E
author: Wenjie Zhu
author: Qin Meng Zhao
publication date: 1993-02-22T00:00:00Z
review text: A three-stage difference technique for ordinary differential equations is described. It consist of three implicit steps performed by using either the trapezoidal or the mid-point rule with proper step sizes. The fourth order accuracy of these schemes is derived from the general theory based on a Lie series and the concept of self-adjoint operators. The stability analysis of the three-stage schemes is presented. It is shown that though the scheme is not \(A\)-stable, the instability region in the complex plane is a little disc on the real axis thus providing stability for systems which have eigenvalues not very adjacent to the real axis. Numerical tests for Hamiltonian systems and stiff systems of ordinary differential equations are described to show the accuracy and the stability of the schemes.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34E13
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 120307
zbMATH Keywords: three-stage difference scheme
zbMATH Keywords: fourth order accuracy
zbMATH Keywords: Lie series
zbMATH Keywords: self- adjoint operators
zbMATH Keywords: stability
zbMATH Keywords: instability region
zbMATH Keywords: Numerical tests
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: stiff systems
reviewed by: A. I. Tolstykh
describes a project that uses: RODAS
MaRDI profile type: Publication
cites work: Q3779682
cites work: Lie series and invariant functions for analytic symplectic maps
cites work: Q3789492
cites work: Lie series and nonlinear ordinary differential equations
cites work: Q4167627
cites work: Hamiltonian algorithms for Hamiltonian systems and a comparative numerical study
cites work: Q5719651
full work available at URL: 0898-1221(93)90209-e
OpenAlex ID: W2093341162
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 120307