Weak delay-dependent stability of Runge-Kutta methods for differential systems with distributed delays

This paper discusses the stability of Runge-Kutta methods for differential systems with distributed delays. Weak delay-dependent stability of Pouzet-type Runge-Kutta methods is studied in this paper. It is revealed that under suitable conditions, Runge-Kutta methods preserve weak delay-dependent stability. An algorithm is employed to check weak delay-dependent stability of numerical solutions. And the effectiveness of the derived theoretical results is demonstrated with numerical examples.