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Newton--Cotes formulae for long-time integration. (English) Zbl 1041.65104
This paper proposes linear multistep methods based on closed Newton-Cotes formulae for solving Hamiltonian problems. The analysis is very brief and considers only a trivial linear problem and seems to contradict theory on the general applicability of linear multistep methods for Hamiltonian problems.

65P10Numerical methods for Hamiltonian systems including symplectic integrators
37M15Symplectic integrators (dynamical systems)
Full Text: DOI
[1] Arnold, V.: Mathematical methods of classical mechanics. (1978) · Zbl 0386.70001
[2] Chiou, J. C.; Wu, S. D.: Open Newton--cotes differential methods as multilayer symplectic integrators. J. chem. Phys. 107, 6894-6897 (1997)
[3] Sanz-Serna, J. M.; Calvo, M. P.: Numerical Hamiltonian problem. (1994) · Zbl 0816.65042
[4] T.E. Simos, Numerical Methods for 1D, 2D and 3D Differential Equations Arising in Chemical Problems, in: A. Hinchliffe (Ed.), Chemical Modelling: Applications and Theory, Roy. Soc. Chem., 2002, pp. 170--270.
[5] Zhu, W.; Zhao, X.; Tang, Y.: Numerical methods with a high order of accuracy in the quantum system. J. chem. Phys. 104, 2275-2286 (1996)