In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK me...In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK methods of arbitrarily high order, which are based on the composite algorithm, are constructed. In particular, the symplectically composite PRK methods of arbitrarily high order become explicit when applied to separable Hamiltonian systems.展开更多
A characterization of linear symplectic Runge-Kutta methods, which is based on the W-transformation of Hairer and Wanner, is presented. Using this characterization three classes of high order linear symplectic Runge-K...A characterization of linear symplectic Runge-Kutta methods, which is based on the W-transformation of Hairer and Wanner, is presented. Using this characterization three classes of high order linear symplectic Runge-Kutta methods are constructed. They include and extend known classes of high order linear symplectic Runge-Kutta methods.展开更多
文摘In this paper three classes of high order symplectic partitioned Runge-Kutta (PRK) methods, which are based on the W-transformation of Hairer and Wanner, and a particular class of diagonally implicit symplectic PRK methods of arbitrarily high order, which are based on the composite algorithm, are constructed. In particular, the symplectically composite PRK methods of arbitrarily high order become explicit when applied to separable Hamiltonian systems.
基金This work has been supported by the Swiss National Science Foundation.
文摘A characterization of linear symplectic Runge-Kutta methods, which is based on the W-transformation of Hairer and Wanner, is presented. Using this characterization three classes of high order linear symplectic Runge-Kutta methods are constructed. They include and extend known classes of high order linear symplectic Runge-Kutta methods.
