02408nmm 2200000 a 4500 3263 ART--2009-001 eng Calvo, M. calvo@unizar.es On explicit multi-revolution Runge–Kutta schemes 2007-01-01 mult. p 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. initial value problems with almost periodic or highly oscillatory solutions Runge–Kutta methods long term integration multi-revolution methods Montijano, Juan I. monti@unizar.es Rández, Luis randez@unizar.es Vol. 26, Num. 1-3 (Enero 2007) Adv. Comput. Math. Advances in Computational Mathematics 1572-9044 miguelm@unizar.es http://dx.doi.org/10.1007/s10444-004-7209-z Texto completo oai:zaguan.unizar.es:3263 driver Matemática Aplicada ART ANyA international_article international_article