Delay-dependent stability of a class of Runge-Kutta methods for delay differential equations with distributed delays

This paper introduces a class of Time-Accurate and highly-Stable Explicit Runge-Kutta schemes for solving delay differential equations with distributed delays. The delay terms are approximated using Lagrange interpolation. Then, by applying the argument principle, the delay-dependent stability criteria of the numerical methods are derived. Two numerical examples are given to demonstrate that the proposed methods exhibit larger stability regions compared to explicit Runge-Kutta methods. The validity of the stability criteria is also verified.