eng Calvo, M. Montijano, Juan I. Rández, Luis On explicit multi-revolution Runge–Kutta schemes initial value problems with almost periodic or highly oscillatory solutions Runge–Kutta methods long term integration multi-revolution methods 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. 2009-05-05T09:30:55Z http://zaguan.unizar.es/record/3263 info:eu-repo/semantics/publishedVersion Zaragoza Researchers Students Librarians