Asymptotic Stability Properties of $\theta$-Methods for the Multi-Pantograph Delay Differential Equation
Year: 2004
Author: Dongsong Li, Mingzhu Liu
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 381–388
Abstract
This paper deals with the asymptotic stability analysis of $\theta$ – methods for multi-pantograph delay differential equation
Here $\lambda, μ_1,μ_2, ... , μ_l, u_0 \in C$.
In recent years stability properties of numerical methods for this kind of equation has been studied by numerous authors. Many papers are concerned with meshes with fixed stepsize. In general the developed techniques give rise to non-ordinary recurrence relation. In this work, instead,we study constrained variable stpesize schemes, suggested by theoretical and computational reasons, which lead to a non-stationary difference equation. A general theorem is presented which can be used to obtain the characterization of the stability regions of $\theta$ – methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10312
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 381–388
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 8
Keywords: $\theta$ – methods Asymptotic stability Multi-pantograph delay differential equations.