Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage

Wensheng Tang, Guangming Lang and Xuqiong Luo

Applied Mathematics and Computation, 2016, vol. 286, issue C, 279-287

Abstract: Hamiltonian systems, as one of the most important class of dynamical systems, are associated with a well-known geometric structure called symplecticity. Symplectic numerical algorithms, which preserve such a structure are therefore of interest. In this article, we study the construction of symplectic (partitioned) Runge–Kutta methods with continuous stage. This construction of symplectic methods mainly relies upon the expansion of orthogonal polynomials and the simplifying assumptions for (partitioned) Runge–Kutta type methods. By using suitable quadrature formulae, it also provides a new and simple way to construct symplectic (partitioned) Runge–Kutta methods in classical sense.

Keywords: Hamiltonian systems; Symplectic methods; Continuous-stage Runge–Kutta methods; Continuous-stage partitioned Runge–Kutta methods (search for similar items in EconPapers)
Date: 2016
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:286:y:2016:i:c:p:279-287

DOI: 10.1016/j.amc.2016.04.026

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