TY - JOUR
T1 - $\mathcal{H}$-Stability of Runge-Kutta Methods with Variable Stepsize for System of Pantograph Equations
AU - Xu , Yang
AU - Zhao , Jingjun
AU - Liu , Mingzhu
JO - Journal of Computational Mathematics
VL - 5
SP - 727
EP - 734
PY - 2004
DA - 2004/10
SN - 22
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jcm/10299.html
KW - Delay differential equations, Stability, Runge-Kutta method.
AB - <p style="text-align: justify;">This paper deals with $\mathcal{H}$-stability of Runge-Kutta methods with variable stepsize for the system of pantograph equations. It is shown that both Runge-Kutta methods with nonsingular matrix coefficient $A$ and stiffly accurate Runge-Kutta methods are $\mathcal{H}$-stable if and only if the modulus of stability function at infinity is less than 1.</p>