The Numerical Stability of the $\theta$-Method for Delay Differential Equations with Many Variable Delays

The Numerical Stability of the $\theta$-Method for Delay Differential Equations with Many Variable Delays

Year:    1999

Author:    Lin Qiu, Taketomo Mitsui, Jiao-Xun Kuang

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 5 : pp. 523–532

Abstract

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs)

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where $a, b_1, b_2, ... b_m$ and $y_0 \in C, 0 < \lambda_m \le \lambda_{m-1} \le ... \le \lambda_1<1$. A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear $\theta$-method is $\bigwedge GP_m$-stable if and only if $\frac{1}{2} \le \theta \le 1$.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/1999-JCM-9122

Journal of Computational Mathematics, Vol. 17 (1999), Iss. 5 : pp. 523–532

Published online:    1999-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Delay differential equation Variable delays Numerical stability $\theta$-methods.

Author Details

Lin Qiu

Taketomo Mitsui

Jiao-Xun Kuang