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Stability analysis of Runge-Kutta methods for differential equations with piecewise continuous arguments of mixed type. (English) Zbl 1220.65105
Authors’ abstract: This paper deals with the stability analysis of the Runge-Kutta methods for a differential equation with piecewise continuous arguments of mixed type. The stability regions of the analytical solution are given. The necessary and sufficient conditions under which the numerical solution is asymptotically stable are discussed. The conditions under which the analytical stability region is contained in the numerical stability region are obtained and some numerical experiments are given.
MSC:
65L20Stability and convergence of numerical methods for ODE
65L06Multistep, Runge-Kutta, and extrapolation methods
65M12Stability and convergence of numerical methods (IVP of PDE)
65L07Numerical investigation of stability of solutions of ODE