Numerical intergration of perturbed linear systems
type: Item
instance of: scholarly article
title: Numerical intergration of perturbed linear systems
zbMATH Open document ID: 0938.65093
DOI: 10.1016/S0168-9274(98)00126-3
author: Pablo Martín
author: José M. Ferrándiz
published in: Applied Numerical Mathematics
publication date: 2000-02-08T00:00:00Z
review text: The paper deals with numerical integration of the perturbed system of differential equations of the form \[ x'=Ax+\varepsilon g(x,t),\qquad x(0)=x_0, \tag{1} \] where \(x:{\mathbb R}\to {\mathbb R}^m, g:{\mathbb R}\times {\mathbb R}\to {\mathbb R}^m\) and \(A\) is a constant \(m\times m\) matrix. The authors suggest new explicit and implicit multistep algorithms for the integration of (1) based on the method of \textit{G. Scheifele} [Z. Angew. Math. Phys. 22, 186-210 (1971; Zbl 0221.56135)]. In order to avoid difficult preliminary computations of coefficients required for the implementation of the Scheifele method, the latter is transformed into a multistep scheme with the good properties of the original method preserved. Some numerical examples are presented to illustrate the advantage of a new method over the classical ones like Adams or Runge-Kutta methods.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 1367739
zbMATH Keywords: multistep methods
zbMATH Keywords: perturbed linear system
zbMATH Keywords: Scheifele method
zbMATH Keywords: comparison of methods
zbMATH Keywords: Adams method
zbMATH Keywords: numerical examples
zbMATH Keywords: Runge-Kutta methods
reviewed by: Yuriy V. Rogovchenko
MaRDI profile type: Publication
full work available at URL: s0168-9274(98)00126-3
OpenAlex ID: W2059065552
description: scientific article; zbMATH DE number 1367739