This paper is concerned with stability analysis of additive Runge-Kutta methods for delay-integro-differential equations. We show that if the additive Runge-Kutta methods are algebraically stable, the perturbations of the numerical solutions are controlled by the initial perturbations from the system and the methods.
Hongyu Qin. Zhiyong Wang. Fumin Zhu. Jinming Wen. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations." Int. J. Differ. Equ. 2018 (SI2) 1 - 5, 2018. https://doi.org/10.1155/2018/8241784