Numerical Integration by the 2-Stage Diagonally Implicit Runge-Kutta Method for Electromagnetic Transient Simulations

2009 ◽  
Vol 24 (1) ◽  
pp. 390-399 ◽  
Author(s):  
T. Noda ◽  
K. Takenaka ◽  
T. Inoue
Keyword(s):  
Numerical Integration ◽  
Kutta Method ◽  
Electromagnetic Transient ◽  
Runge Kutta Method ◽  
Transient Simulations ◽  
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.

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