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

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