Year: 2001
Author: Hong-Jiong Tian, Jiao-Xun Kuang, Lin Qiu
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 2 : pp. 125–130
Abstract
This paper deals with the numerical solution of initial value problems for systems of neutral differential equations y′(t)=f(t,y(t),y(t−τ),y′(t−τ)),t＞0, y(t)=φ(t) t＜0, where τ＞0,f and φ denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y′(t)=Ay(t)+By(t−τ)+Cy′(t−τ), where A,B and C denote constant complex N×N-matrices, and τ＞0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if it is A-stable for ordinary differential equations.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2001-JCM-8963
Journal of Computational Mathematics, Vol. 19 (2001), Iss. 2 : pp. 125–130
Published online: 2001-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: Numerical stability Linear multistep method Delay differential equations.