Article ID Journal Published Year Pages File Type
4625746 Applied Mathematics and Computation 2016 9 Pages PDF
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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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