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Volume 14, Issue 3
The Stability Analysis of the $θ$-Methods for Delay Differential Equations

H. J. Tian & J. X. Kuang

J. Comp. Math., 14 (1996), pp. 203-212.

Published online: 1996-06

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  • Abstract

This paper deals with the stability analysis of $\theta -$methods for the numerical solution of delay differential equations (DDEs). We focus on the behaviour of such methods in the solution of the linear test equation $y^{\prime}(t)=a(t)y(t)+b(t)y(t-\tau )$, where $\tau >0$, $a(t)$ and $b(t)$ are functions from $R$ to $C$. It is proved that the linear $\theta -$method and the one-leg $\theta -$method are TGP-stable if and only if $\theta =1.$

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@Article{JCM-14-203, author = {H. J. Tian and J. X. Kuang}, title = {The Stability Analysis of the $θ$-Methods for Delay Differential Equations}, journal = {Journal of Computational Mathematics}, year = {1996}, volume = {14}, number = {3}, pages = {203--212}, abstract = {

This paper deals with the stability analysis of $\theta -$methods for the numerical solution of delay differential equations (DDEs). We focus on the behaviour of such methods in the solution of the linear test equation $y^{\prime}(t)=a(t)y(t)+b(t)y(t-\tau )$, where $\tau >0$, $a(t)$ and $b(t)$ are functions from $R$ to $C$. It is proved that the linear $\theta -$method and the one-leg $\theta -$method are TGP-stable if and only if $\theta =1.$

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9231.html} }
TY - JOUR T1 - The Stability Analysis of the $θ$-Methods for Delay Differential Equations AU - H. J. Tian & J. X. Kuang JO - Journal of Computational Mathematics VL - 3 SP - 203 EP - 212 PY - 1996 DA - 1996/06 SN - 14 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9231.html KW - AB -

This paper deals with the stability analysis of $\theta -$methods for the numerical solution of delay differential equations (DDEs). We focus on the behaviour of such methods in the solution of the linear test equation $y^{\prime}(t)=a(t)y(t)+b(t)y(t-\tau )$, where $\tau >0$, $a(t)$ and $b(t)$ are functions from $R$ to $C$. It is proved that the linear $\theta -$method and the one-leg $\theta -$method are TGP-stable if and only if $\theta =1.$

H. J. Tian and J. X. Kuang. (1996). The Stability Analysis of the $θ$-Methods for Delay Differential Equations. Journal of Computational Mathematics. 14 (3). 203-212. doi:
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