Volume 17, Issue 5
The Numerical Stability of the Theta-Method for Delay Differential Equations with Many Variable Delays

Lin Qiu, Taketomo Mitsui & Jiao Xun Kuang

DOI:

J. Comp. Math., 17 (1999), pp. 523-532

Published online: 1999-10

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  • Abstract

This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs):y'(t) =ay(t) + Sum DD(m, j = 1 .. b_jy(lambda_jt) t >= y_0, where a, b_1, b_2, ... b_m and y_0 \in C, 0 > lambda_m \le \lambda_m-1 \le ... \le \lambda_1). A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear theta-method is OmegaGP_m-stable if and only if SX 1 2 SX \le theta \le 1.

  • Keywords

Delay differential equation Variable delays Numerical stability

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@Article{JCM-17-523, author = {}, title = {The Numerical Stability of the Theta-Method for Delay Differential Equations with Many Variable Delays}, journal = {Journal of Computational Mathematics}, year = {1999}, volume = {17}, number = {5}, pages = {523--532}, abstract = { This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs):y'(t) =ay(t) + Sum DD(m, j = 1 .. b_jy(lambda_jt) t >= y_0, where a, b_1, b_2, ... b_m and y_0 \in C, 0 > lambda_m \le \lambda_m-1 \le ... \le \lambda_1). A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear theta-method is OmegaGP_m-stable if and only if SX 1 2 SX \le theta \le 1. }, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9122.html} }
TY - JOUR T1 - The Numerical Stability of the Theta-Method for Delay Differential Equations with Many Variable Delays JO - Journal of Computational Mathematics VL - 5 SP - 523 EP - 532 PY - 1999 DA - 1999/10 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9122.html KW - Delay differential equation KW - Variable delays KW - Numerical stability AB - This paper deals with the asymptotic stability of theoretical solutions and numerical methods for the delay differential equations (DDEs):y'(t) =ay(t) + Sum DD(m, j = 1 .. b_jy(lambda_jt) t >= y_0, where a, b_1, b_2, ... b_m and y_0 \in C, 0 > lambda_m \le \lambda_m-1 \le ... \le \lambda_1). A sufficient condition such that the differential equations are asymptotically stable is derived. And it is shown that the linear theta-method is OmegaGP_m-stable if and only if SX 1 2 SX \le theta \le 1.
Lin Qiu, Taketomo Mitsui & Jiao Xun Kuang. (1970). The Numerical Stability of the Theta-Method for Delay Differential Equations with Many Variable Delays. Journal of Computational Mathematics. 17 (5). 523-532. doi:
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