A SIXTH ORDER DIAGONALLY IMPLICIT SYMMETRIC AND SYMPLECTIC RUNGE-KUTTA METHOD FOR SOLVING HAMILTONIAN SYSTEMS

Chengxiang Jiang; Yuhao Cong

doi:10.11948/2015014

2015 Volume 5 Issue 1

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Chengxiang Jiang, Yuhao Cong. A SIXTH ORDER DIAGONALLY IMPLICIT SYMMETRIC AND SYMPLECTIC RUNGE-KUTTA METHOD FOR SOLVING HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 159-167. doi: 10.11948/2015014

Citation:

Chengxiang Jiang, Yuhao Cong. A SIXTH ORDER DIAGONALLY IMPLICIT SYMMETRIC AND SYMPLECTIC RUNGE-KUTTA METHOD FOR SOLVING HAMILTONIAN SYSTEMS[J]. Journal of Applied Analysis & Computation, 2015, 5(1): 159-167. doi: 10.11948/2015014

A SIXTH ORDER DIAGONALLY IMPLICIT SYMMETRIC AND SYMPLECTIC RUNGE-KUTTA METHOD FOR SOLVING HAMILTONIAN SYSTEMS

Department of Mathematics, Shanghai Normal University, Shanghai 200234, China

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Abstract

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 scientific literature.
- Oscillatory Hamiltonian system /
- symplecticness /
- symmetric /
- Pstable /
- Runge-Kutta method
MSC: 65L06

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