3268 ART--2009-003 eng Calvo, M. calvo@unizar.es Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods 2004 mult. p 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 multi-revolution methods Runge-Kutta Butcher compositions of a near identity map Jay, J.O. ljay@math.uiowa.edu Montijano, Juan I. monti@unizar.es Rández, Luis randez@unizar.es Numerische Mathematik Numer. Math. 0945-3245 Vol. 97, Num. 4 (junio 2004), pp. 635-666 teresa@unizar.es Matemática Aplicada ART ANyA international_article oai:zaguan.unizar.es:3268 driver http://dx.doi.org/10.1007/s00211-004-0518-9 Texto completo