Stability of some continuously imbedded Runge-Kutta methods of Sarafyan

Abstract

AbstractSarafyan and others have recently developed novel explicit Runge-Kutta methods. Associated with each method is an imbedded polynomial which interpolates the Runge-Kutta method and which is itself a Runge-Kutta approximation at non-meshpoints. In this paper, we show that the interpolation polynomials possess the desirable stability properties of the Runge-Kutta methods