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Volume 5, Number 1, 2015, Pages 159-167                                                                DOI:10.11948/2015014
A sixth order diagonally implicit symmetric and symplectic Runge-Kutta method for solving Hamiltonian systems
Chengxiang Jiang,Yuhao Cong
Keywords:Oscillatory Hamiltonian system
Abstract:
      The paper is concerned with construction of symmetric and symplectic Runge-Kutta methods for Hamiltonian systems. Based on the symplectic and symmetrical properties, a sixth-order diagonally implicit symmetric and symplectic Runge-Kutta method with seven stages is presented, the proposed method proved to be P-stable. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing Runge-Kutta methods in scientic literature.
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