The Stability of the $θ$-Methods for Delay Differential Equations

The Stability of the $θ$-Methods for Delay Differential Equations

Year:    1999

Author:    Jing-Jun Zhao, Ming-Zhu Liu, Shen-Shan Qiu

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 4 : pp. 441–448

Abstract

This paper deals with the stability analysis of numerical methods for the solution of delay differential equations. We focus on the behaviour of three $θ$-methods in the solution of the linear test equation $u'(t)=A(t)u(t)+B(t)u(τ(t))$ with $τ(t)$ and $A(t), B(t)$ continuous matrix functions. The stability regions for the three $θ$-methods are determined.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1999-JCM-9115

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 4 : pp. 441–448

Published online:    1999-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    8

Keywords:    Delay differential equations Numerical solution Stability $θ$-methods.

Author Details

Jing-Jun Zhao

Ming-Zhu Liu

Shen-Shan Qiu