A Class of Two-Step Continuity Runge-Kutta Methods for Solving Singular Delay Differential Equations and Its Stability Analysis (Journal of Computational Mathematics, 2021)
In this paper, a class of two-step continuity Runge-Kutta (TSCRK) methods for solvingsingular delay differential equations (DDEs) is presented. Analysis of numerical stability ofthe methods is given. We consider the two distinct cases: $(i)τ ≥ h$, $(ii)τ < h$, where thedelay $τ$ 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 showthe efficiency of the method.
Keywords: Analysis of numerical stability; Singular delay differential equations; Two-step continuity Runge-Kutta methods.