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

2015 ◽  
Vol 5 (1) ◽  
pp. 159-167
Author(s):  
Chengxiang Jiang ◽  
◽  
Yuhao Cong
Keyword(s):  
Hamiltonian Systems ◽  
Sixth Order ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

Symplectic Partitioned Runge-Kutta and Symplectic Runge-Kutta Methods Generated by 2-Stage RadauIA Method

2013 ◽  
Vol 444-445 ◽  
pp. 633-636
Author(s):  
Jia Bo Tan
Keyword(s):  
Numerical Integration ◽  
Hamiltonian Systems ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

To preserve the symplecticity property, it is natural to require numerical integration of Hamiltonian systems to be symplectic. As a famous numerical integration, it is known that the 2-stage RadauIA method is not symplectic. With the help of symplectic conditions of Runge-Kutta method and partitioned Runge-Kutta method, a symplectic partitioned Runge-Kutta method and a symplectic Runge-Kutta method are constructed on the basis of 2-stage RadauIA method in this paper.

A sixth order symmetric and symplectic diagonally implicit Runge-Kutta method

2014 ◽  
Author(s):  
Zacharoula Kalogiratou ◽  
Theodore Monovasilis ◽  
T. E. Simos
Keyword(s):  
Sixth Order ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Runge Kutta

scholarly journals Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Y. H. Cong ◽  
C. X. Jiang
Keyword(s):  
Numerical Integration ◽  
Hamiltonian Systems ◽  
Numerical Experiments ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Oscillating Solutions ◽  
Dispersion Order ◽  
Algebraic Order ◽  
Runge Kutta

The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.

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