A symplectic exponentially fitted modified Runge–Kutta–Nyström method for the numerical integration of orbital problems

New Astronomy ◽  
2005 ◽  
Vol 10 (4) ◽  
pp. 261-269 ◽  
Author(s):  
Hans Van de Vyver
Keyword(s):  
Numerical Integration ◽  
Nyström Method ◽  
Nystrom Method ◽  
Orbital Problems ◽  
Exponentially Fitted ◽  
Runge Kutta

Transient Stability Simulation by Explicit and Symplectic Runge-Kutta-Nyström Method

2011 ◽  
Vol 383-390 ◽  
pp. 1960-1964
Author(s):  
Fang Zong Wang ◽  
Yi Fan He ◽  
Jing Ye
Keyword(s):  
Differential Equations ◽  
Power System ◽  
Numerical Integration ◽  
Transient Stability ◽  
Kutta Method ◽  
Nyström Method ◽  
Nystrom Method ◽  
Runge Kutta Method ◽  
Numerical Integration Methods ◽  
Runge Kutta

The symplectic algorithm is a kind of new numerical integration methods. This paper proposes the application of the explicit and symplectic Runge-Kutta-Nyström method to solve the differential equations encountered in the power system transient stability simulation. The proposed method achieves significant improvement both in speed and in calculation precision as compared to the conventional Runge-Kutta method which is widely used for power system transient stability simulation. The proposed method is applied to the IEEE 145-bus system and the results are reported.

scholarly journals The Use of Phase Lag and Amplification Error Derivatives for the Construction of a Modified Runge-Kutta-Nyström Method

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
D. F. Papadopoulos ◽  
T. E. Simos
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Numerical Results ◽  
Phase Lag ◽  
Nyström Method ◽  
Nystrom Method ◽  
Modified Method ◽  
Algebraic Order ◽  
Runge Kutta

A new modified Runge-Kutta-Nyström method of fourth algebraic order is developed. The new modified RKN method is based on the fitting of the coefficients, due to the nullification not only of the phase lag and of the amplification error, but also of their derivatives. Numerical results indicate that the new modified method is much more efficient than other methods derived for solving numerically the Schrödinger equation.

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