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International Journal of Differential Equations
Volume 2013 (2013), Article ID 681575, 10 pages
Nonlinear Extension of Multiproduct Expansion Schemes and Applications to Rigid Bodies
University of Greifswald, Institute of Physics, Felix-Hausdorff-Str. 6, 17489 Greifswald, Germany
Received 25 April 2013; Accepted 5 August 2013
Academic Editor: Sanjay Khattri
Copyright © 2013 Jürgen Geiser. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. V. Berry, “The levitron: an adiabatic trap for Spins,” Proceedings of the Royal Society A, vol. 452, pp. 1207–1220, 1996.
- H. R. Dullin and R. W. Easton, “Stability of levitrons,” Physica D, vol. 126, no. 1-2, pp. 1–17, 1999.
- J. Geiser, “Multiscale methods for levitron problems: theory and applications,” Computers and Structures, vol. 122, pp. 27–32, 2013.
- S. Blanes, F. Casas, J. A. Oteo, and J. Ros, “The Magnus expansion and some of its applications,” Physics Reports, vol. 470, no. 5-6, pp. 151–238, 2009.
- F. Casas and A. Iserles, “Explicit Magnus expansions for nonlinear equations,” Journal of Physics A, vol. 39, no. 19, pp. 5445–5461, 2006.
- S. A. Chin and J. Geiser, “Multi-product operator splitting as a general method of solving autonomous and nonautonomous equations,” IMA Journal of Numerical Analysis, vol. 31, no. 4, pp. 1552–1577, 2011.
- S. A. Chin and P. Anisimov, “Gradient symplectic algorithms for solving the radial schrödinger equation,” Journal of Chemical Physics, vol. 124, no. 5, Article ID 054106, 2006.
- G. Strang, “On the construction and comparison of difference schemes,” SIAM Journal on Numerical Analysis, vol. 5, pp. 506–517, 1968.
- E. Hairer, C. Lubich, and G. Wanner, Geometric Numerical Integration Structure-Preserving Algorithms for Ordinary Differential Equations, vol. 31 of Springer Series in Computational Mathematics, Springer, Berlin, Germany, 2002.
- J. Geiser, G. Tanoğlu, and N. Gücüyenen, “Higher order operator splitting methods via Zassenhaus product formula: theory and applications,” Computers & Mathematics with Applications, vol. 62, no. 4, pp. 1994–2015, 2011.
- J. Geiser and G. Tanoglu, “Operator-splitting methods via the Zassenhaus product formula,” Applied Mathematics and Computation, vol. 217, no. 9, pp. 4557–4575, 2011.
- D. Scholz and M. Weyrauch, “A note on the Zassenhaus product formula,” Journal of Mathematical Physics, vol. 47, no. 3, Article ID 033505, 7 pages, 2006.
- C. T. Kelley, Iterative Methods for Linear and Nonlinear Equations, vol. 16 of Frontiers in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1995.
- S. A. Chin, “Symplectic and energy-conserving algorithms for solving magnetic field trajectories,” Physical Review E, vol. 77, no. 6, Article ID 066401, 12 pages, 2008.
- H. Goldstein, Classical Mechanics, Addison-Wesley Press, Cambridge, Mass, USA, 3rd edition, 1951.
- R. F. Gans, T. B. Jones, and M. Washizu, “Dynamics of the Levitron,” Journal of Physics D, vol. 31, pp. 671–679, 1998.