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Keywords = explicit symplectic Runge–Kutta–Nyström methods

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13 pages, 819 KB  
Article
Explicit Symplectic Runge–Kutta–Nyström Methods Based on Roots of Shifted Legendre Polynomial
by Jun Zhang, Jingjing Zhang and Shangyou Zhang
Mathematics 2023, 11(20), 4291; https://doi.org/10.3390/math11204291 - 15 Oct 2023
Cited by 1 | Viewed by 1583
Abstract
To date, all explicit symplectic Runge–Kutta–Nyström methods of order five or above are derived by numerical solutions of order condition equations and symplectic condition. In this paper, we derive 124 sets of seven-stage fifth-order explicit symplectic Runge–Kutta–Nyström methods with closed-form coefficients in the [...] Read more.
To date, all explicit symplectic Runge–Kutta–Nyström methods of order five or above are derived by numerical solutions of order condition equations and symplectic condition. In this paper, we derive 124 sets of seven-stage fifth-order explicit symplectic Runge–Kutta–Nyström methods with closed-form coefficients in the Butcher tableau using the roots of a degree-3 shifted Legendre polynomial. One method is analyzed and its P-stable interval is derived. Numerical tests on the two newly discovered methods are performed, showing their long-time stability and large step size stability over some existing methods. Full article
(This article belongs to the Special Issue Computational Mathematics and Numerical Analysis)
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