✦ LIBER ✦

Stability and oscillations of numerical solutions for differential equations with piecewise continuous arguments of alternately advanced and retarded type

✍ Scribed by Qi Wang; Qingyong Zhu; Mingzhu Liu

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 361 KB
Volume: 235
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2010.08.041

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✦ Synopsis

This paper is concerned with the numerical properties of θ-methods for the solution of alternately advanced and retarded differential equations with piecewise continuous arguments. Using two θ -methods, namely the one-leg θ-method and the linear θ-method, the necessary and sufficient conditions under which the analytic stability region is contained in the numerical stability region are obtained, and the conditions of oscillations for the θ -methods are also obtained. It is proved that oscillations of the analytic solution are preserved by the θ -methods. Furthermore, the relationships between stability and oscillations are revealed. Some numerical experiments are presented to illustrate our results.

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