High order symplectic integrators based on continuous-stage Runge-Kutta-Nyström methods. (English) Zbl 1429.65299
Summary: On the basis of the previous work by the first and the last authors [ibid. 323, 204–219 (2018; Zbl 1426.65203)], in this paper, we present a more effective way to construct high-order symplectic integrators for solving second order Hamiltonian equations. Instead of analyzing order conditions step by step as shown in the previous work, the new technique of this paper is using Legendre expansions to deal with the simplifying assumptions for order conditions. With the new technique, high-order symplectic integrators can be conveniently devised by truncating an orthogonal series.
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
continuous-stage Runge-Kutta-Nyström methods; Hamiltonian systems; symplectic integrators; Legendre polynomial expansion; simplifying assumptionsCitations:
Zbl 1426.65203Software:
LIMbookReferences:
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