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Liu, Changying; Li, Jiayin; Yang, Zhenqi; Tang, Yumeng; Liu, Kai

Two high-order energy-preserving and symmetric Gauss collocation integrators for solving the hyperbolic Hamiltonian systems. (English) Zbl 1540.65529

Math. Comput. Simul. 205, 19-32 (2023).
Summary: In this paper, we first derive the energy-preserving collocation integrator for solving the hyperbolic Hamiltonian systems. Then, two concrete high-order energy-preserving and symmetric integrators are presented by choosing the collocation nodes as two and three Gauss-Legendre points, respectively. The convergence and the symmetry of the constructed energy-preserving integrators are rigorously analysed. Numerical results verify the energy conservation property and the accuracy of the proposed integrators.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations

Keywords:

hyperbolic Hamiltonian system; energy preservation; Gauss collocation integrator; continuous-stage Runge-Kutta-Nyström methods
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Full Text: DOI

References:

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