On the generation of P-stable exponentially fitted Runge-Kutta-Nyström methods by exponentially fitted Runge-Kutta methods

Authors:
Hans Van de Vyver
Affiliations:
Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium
Venue:
Journal of Computational and Applied Mathematics
Year:
2006

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Abstract

This paper provides an investigation of the stability properties of a family of exponentially fitted Runge-Kutta-Nystrom (EFRKN) methods. P-stability is a very important property usually demanded for the numerical solution of stiff oscillatory second-order initial value problems. P-stable EFRKN methods with arbitrary high order are presented in this work. We have proved our results based on a symmetry argument.