Numerical Stability and Oscillations of Runge-Kutta Methods for Differential Equations with Piecewise Constant Arguments of Advanced Type (Communications in Mathematical Research, 2021)
For differential equations with piecewise constant arguments of advancedtype, numerical stability and oscillations of Runge-Kutta methods are investigated.The necessary and sufficient conditions under which the numerical stability regioncontains the analytic stability region are given. The conditions of oscillations for theRunge-Kutta methods are obtained also. We prove that the Runge-Kutta methodspreserve the oscillations of the analytic solution. Moreover, the relationship betweenstability and oscillations is discussed. Several numerical examples which confirm theresults of our analysis are presented.