02408nmm 2200000 a 4500 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
Vol. 97, Num. 4 (junio 2004), pp. 635-666
Numer. Math.
Numerische Mathematik
0945-3245
teresa@unizar.es
http://dx.doi.org/10.1007/s00211-004-0518-9
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