@Article{JCM-17-5, author = {Qiu, Lin and Taketomo, Mitsui and Kuang, Jiao-Xun}, 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)

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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 $\frac{1}{2} \le \theta \le 1$.

}, issn = {1991-7139}, doi = {https://doi.org/1999-JCM-9122}, url = {https://global-sci.com/article/85648/the-numerical-stability-of-the-theta-method-for-delay-differential-equations-with-many-variable-delays} }