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Force-gradient nested multirate methods for Hamiltonian systems. (English) Zbl 1348.65177

Summary: Force-gradient decomposition methods are used to improve the energy preservation of symplectic schemes applied to Hamiltonian systems. If the potential is composed of different parts with strongly varying dynamics, this multirate potential can be exploited by coupling force-gradient decomposition methods with splitting techniques for multi-time scale problems to further increase the accuracy of the scheme and reduce the computational costs. In this paper, we derive novel force-gradient nested methods and test them numerically. We apply them on the three-body problem, modified for a better observation of the advantageous properties, needed for the future research.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
65D30 Numerical integration
37M99 Approximation methods and numerical treatment of dynamical systems
34C60 Qualitative investigation and simulation of ordinary differential equation models
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