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000003268 001__ 3268
000003268 037__ $$aART--2009-003
000003268 041__ $$aeng
000003268 100__ $$aCalvo, M.$$
000003268 245__ $$aApproximate compositions of a near identity map by multi-revolution Runge-Kutta methods 
000003268 260__ $$c2004
000003268 300__ $$amult. p
000003268 520__ $$aThe 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
000003268 6531_ $$amulti-revolution methods
000003268 6531_ $$aRunge-Kutta
000003268 6531_ $$aButcher
000003268 6531_ $$acompositions of a near identity map
000003268 700__ $$aJay, J.O.$$
000003268 700__ $$aMontijano, Juan I.$$
000003268 700__ $$aRández, Luis$$
000003268 773__ $$gVol. 97, Num. 4 (junio 2004), pp. 635-666$$pNumer. Math.$$tNumerische Mathematik$$x0945-3245
000003268 8560_ $$
000003268 8564_ $$u$$zTexto completo
000003268 909CO $$$$pdriver
000003268 9102_ $$a$$bMatemática Aplicada
000003268 980__ $$aART$$bANyA
000003268 983__ $$ainternational_article
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