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Volume 17, Issue 4
The Stability of the $θ$-Methods for Delay Differential Equations

Jing-Jun Zhao, Ming-Zhu Liu & Shen-Shan Qiu

J. Comp. Math., 17 (1999), pp. 441-448.

Published online: 1999-08

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  • 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.

  • Keywords

Delay differential equations, Numerical solution, Stability, $θ$-methods.

  • AMS Subject Headings

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-17-441, author = {Zhao , Jing-JunLiu , Ming-Zhu and Qiu , Shen-Shan}, title = {The Stability of the $θ$-Methods for Delay Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9115.html} }
TY - JOUR T1 - The Stability of the $θ$-Methods for Delay Differential Equations AU - Zhao , Jing-Jun AU - Liu , Ming-Zhu AU - Qiu , Shen-Shan JO - Journal of Computational Mathematics VL - 4 SP - 441 EP - 448 PY - 1999 DA - 1999/08 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9115.html KW - Delay differential equations, Numerical solution, Stability, $θ$-methods. AB -

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.

Zhao , Jing-JunLiu , Ming-Zhu and Qiu , Shen-Shan. (1999). The Stability of the $θ$-Methods for Delay Differential Equations. Journal of Computational Mathematics. 17 (4). 441-448. doi:
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