Métodos Runge-Kutta-Nyström de Pasos Fraccionarios y reducción de orden

Abstract

We study here the order reduction that appears in the numerical integration of second-order in time linear problems by means of Fractional Step Runge-Kutta-Nyström methods. This drawback takes it maximum relevance when the boundary conditions are time dependent. This new kind of methods, introduced in [6] M. J. Moreta, B. Bujanda & J. C. Jorge, Fractional Step Runge-Kutta-Nystr¨om methods, enviado 2007, allows us to combine the advantages of Fractional Step methods with the ones of Runge-Kutta-Nyström methods. We show that this order reduction can be completely avoided,without increasing too much the computational cost, by taking a suitable modification of the classical boundary conditions considered for the internal stages.