Journal article
Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
Numerische Mathematik, Vol.97(4), pp.635-666
06/2004
DOI: 10.1007/s00211-004-0518-9
Abstract
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 φ T N of N near-periods T in terms of the one near-period map φ T evaluated at few s << N selected points. More generally, multi-revolution methods aim at approximating the composition φ N of a near identity map φ. 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.
Details
- Title: Subtitle
- Approximate compositions of a near identity map by multi-revolution Runge-Kutta methods
- Creators
- Manuel Calvo - Departamento de Matemática Aplicada Pza. San Francisco s/n, Universidad de Zaragoza 50009 Zaragoza SpainLaurent O Jay - Department of Mathematics 14 MacLean Hall, The University of Iowa, Iowa City IA 52242-1419 USAJuan I Montijano - Departamento de Matemática Aplicada Pza. San Francisco s/n, Universidad de Zaragoza 50009 Zaragoza SpainLuis Rández - Departamento de Matemática Aplicada Pza. San Francisco s/n, Universidad de Zaragoza 50009 Zaragoza Spain
- Resource Type
- Journal article
- Publication Details
- Numerische Mathematik, Vol.97(4), pp.635-666
- DOI
- 10.1007/s00211-004-0518-9
- ISSN
- 0029-599X
- eISSN
- 0945-3245
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- Language
- English
- Date published
- 06/2004
- Academic Unit
- Mathematics
- Record Identifier
- 9983986092002771
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