Calvo, M. (calvo@unizar.es) ; Montijano, Juan I. (monti@unizar.es) ; Rández, Luis (randez@unizar.es)

Published in:   Advances in Computational Mathematics
  Adv. Comput. Math. Vol. 26, Num. 1-3 (Enero 2007)

Abstract: In this paper, by using the theory of Butcher series, a general expression of the order conditions on the coefficients of a multi-revolution Runge–Kutta method is derived. A complete study of explicit multi-revolution Runge–Kutta methods of order four with four stages is given. Also, by using suitable simplifying assumptions, a family of six stage explicit methods with order five is derived and a particular method of this family (which generalizes the well known formula of order five in DOPRI5(4)) is selected by minimizing a norm of the leading term of the local truncation error. Finally, some numerical experiments are presented to test the behaviour of the new fifth-order method.

Language: eng
Department: Matemática Aplicada

Keyword(s): initial value problems with almost periodic or highly oscillatory solutions ; Runge–Kutta methods ; long term integration ; multi-revolution methods