Abstract
The observer method introduced by Busvelle et al. (1993), is a simple idea that can be used to improve reliable numerical integration of a system of differential equations in the presence of first integrals. In the cited paper the observer method was already tested on some important examples like the Kepler problem and the Gavrilov-Shilnikov system.
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References
Aref H. and Pomprey N., 1982, Integrable and chaotic motions of four vortices I. The case of identical vortices, Proc. R. Soc. London A, 380, 359–387.
Arkhangelsk Yu.A., 1977, Analytical Dynamics of the Rigid Body (in Russian), (Moscow: Nauka).
Arnold V.I., Kozlov V.V. and Neishtadt A.I., 1988, Mathematical aspects of classical and celestial mechanics, in Arnold V.I. (Edit.) Dynamical Systems III, Encyclopaedia of Mathematical Sciences, 3, (Berlin: Springer Verlag).
Busvelle E., Kharab R., Maciejewski A.J. and Strelcyn J.-M., 1993, Numerical Integration of Differential Equations in the Presence of First Integrals: Observer Method, preprint, Rouen University, March 1993.
Butcher J.C., 1964, Implicit Runge-Kutta processes, Math. Comput., 18, 50–64.
Fomenko A.T., 1988, Integrability and nonintegrability in geometry and mechanics, (Dodrecht: Kluwer Academic Publishers).
Golubev V.V., 1953, Lectures on Integration of the Equations of Motion of a Rigid Body about a Fixed Point (in Russian), (Moscow: Gostekhizdat). English translation by the Israel Programme od Scient. Transi. (Jerusalem, 1960).
Hairer E., Norsett S.P. and Wanner G., 1987, Ordinary differential equations I, Nonstiff problem, (Berlin: Springer Verlag).
Kozlov V.V., 1983, Integrability and nonintegrability in hamiltonian mechanics, Russian Math. Survey, 38(1), 1–76.
Pullin D.I. and Saffman P.G., 1991, Long-time symplectic integration: the example of four vortex motion, Proc. R. Soc. London A, 432, 481–494.
Sanz-Serna J.M., 1991, Symplectic integrators for Hamiltonian systems: an overview, Acta Numerica, (annual volume published by Cambridge University Press), 1, 243–286.
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To Janusz Szpotański with deepest admiration.
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Maciejewski, A.J., Strelcyn, JM. (1994). Numerical Integration of Hamiltonian Systems in the Presence of Additional Integrals: Application of the Observer Method. In: Seimenis, J. (eds) Hamiltonian Mechanics. NATO ASI Series, vol 331. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-0964-0_12
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DOI: https://doi.org/10.1007/978-1-4899-0964-0_12
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