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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 9, Pages 1472–1495 (Mi zvmmf11127)  

Testing a new conservative method for solving the Cauchy problem for hamiltonian systems on test problems

P. A. Aleksandrov, G. G. Yelenin

Lomonosov Moscow State University

Abstract: A new numerical method for solving the Cauchy problem for Hamiltonian systems is tested in detail as applied to two benchmark problems: the one-dimensional motion of a point particle in a cubic potential field and the Kepler problem. The global properties of the resulting approximate solutions, such as symplecticity, time reversibility, total energy conservation, and the accuracy of numerical solutions to the Kepler problem are investigated. The proposed numerical method is compared with three-stage symmetric symplectic Runge–Kutta methods, the discrete gradient method, and nested implicit Runge–Kutta methods.

Key words: Hamiltonian systems, numerical methods, energy conservation, symplecticity.

DOI: https://doi.org/10.31857/S0044466920090033


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:9, 1422–1444

Bibliographic databases:

UDC: 519.622.2
Received: 17.04.2017
Revised: 19.12.2019
Accepted:09.04.2020

Citation: P. A. Aleksandrov, G. G. Yelenin, “Testing a new conservative method for solving the Cauchy problem for hamiltonian systems on test problems”, Zh. Vychisl. Mat. Mat. Fiz., 60:9 (2020), 1472–1495; Comput. Math. Math. Phys., 60:9 (2020), 1422–1444

Citation in format AMSBIB
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\issue 9
\pages 1472--1495
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