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 - <p style="text-align: justify;">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 $\tau &gt;0$, $a(t)$ 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 $\theta =1.$</p>