A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis

Abstract

In this paper, a class of two-step continuity Runge-Kutta (TSCRK) methods for solving singular delay differential equations (DDEs) is presented. Analysis of numerical stability of the methods is given. We consider the two distinct cases: $(i)τ ≥ h$, $(ii)τ < h$, where the delay $τ$ and step size $h$ of the two-step continuity Runge-Kutta methods are both constant. The absolute stability regions of some methods are plotted and numerical examples show the efficiency of the method.