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arXiv · 1504.04791

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

Wensheng Tang·Guangming Lang·Xuqiong Luo
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Abstract

Hamiltonian systems are one of the most important class of dynamical systems with a geometric structure called symplecticity and the numerical algorithms which can preserve such geometric structure are of interest. In this article we study the construction of symplectic (partitioned) Runge-Kutta methods with continuous stage, which provides a new and simple way to construct symplectic (partitioned) Runge-Kutta methods in classical sense. This line of construction of symplectic methods relies heavily on the expansion of orthogonal polynomials and the simplifying assumptions for (partitioned) Runge-Kutta type methods.

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Wensheng Tang, Guangming Lang, Xuqiong Luo. 2015-04-19. Construction of symplectic (partitioned) Runge-Kutta methods with continuous stage. https://arxiv.org/abs/1504.04791

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