Stability analysis of one-leg methods for nonlinear functional differential and functional equations
type: Item
instance of: scholarly article
title: Stability analysis of one-leg methods for nonlinear functional differential and functional equations
zbMATH Open document ID: 1202.65087
author: Yuexin Yu
author: Liping Wen
published in: Journal of Computational and Applied Mathematics
publication date: 2010-10-11T00:00:00Z
review text: The aim of this paper is to deal with the numerical methods for a nonlinear system \[ \begin{aligned} y'(t) & = f(t,y(t), y(t-\tau), z(t-\tau))\\ z'(t) & = g(t,y(t), y(t-\tau), z(t-\tau)), t\geq 0 \end{aligned} \] The adaptation of one-leg method is considered for solving systems of nonlinear functional differential and functional equations. It is proved that an \(A\)-stable one-leg method is globally stable and a strongly \(A\)-stable one-leg method is asymptotically stable under suitable conditions. A numerical example is considered to illustrate these results.
Mathematics Subject Classification ID: 65L03
zbMATH DE Number: 5798201
zbMATH Keywords: nonlinear functional differential and functional equations
zbMATH Keywords: one-leg methods
zbMATH Keywords: A-stability
zbMATH Keywords: global stability
zbMATH Keywords: asymptotic stability
reviewed by: R. S. Dahiya
MaRDI profile type: Publication
full work available at URL: j.cam.2010.07.009
OpenAlex ID: W2059427657
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DOI: 10.1016/J.CAM.2010.07.009
description: scientific article; zbMATH DE number 5798201