eng Calvo, M. Jay, J.O. Montijano, Juan I. Rández, Luis Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods multi-revolution methods Runge-Kutta Butcher compositions of a near identity map The so-called multi-revolution methods were introduced in celestial mechanics as an efficient tool for the long-term numerical integration of nearly periodic orbits of artificial satellites around the Earth. A multi-revolution method is an algorithm that approximates the map phgrTN of N near-periods T in terms of the one near-period map phgrT evaluated at few s << N selected points. More generally, multi-revolution methods aim at approximating the composition phgrN of a near identity map phgr. In this paper we give a general presentation and analysis of multi-revolution Runge-Kutta (MRRK) methods similar to the one developed by Butcher for standard Runge-Kutta methods applied to ordinary differential equations. Order conditions, simplifying assumptions, and order estimates of MRRK methods are given. MRRK methods preserving constant Poisson/symplectic structures and reversibility properties are characterized. The construction of high order MRRK methods is described based on some families of orthogonal polynomials. Mathematics Subject Classification (1991): 65L05, 65L06 This material is based upon work supported by the National Science Foundation Grant No. 9983708 and by the DGI Grant BFM2001–2562 2009-05-07T06:07:40Z http://zaguan.unizar.es/record/3268 info:eu-repo/semantics/publishedVersion Zaragoza Researchers Students Librarians