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.