AN ADAPTED SYMPLECTIC INTEGRATOR FOR HAMILTONIAN PROBLEMS

In this paper, a new procedure for deriving efficient symplectic integrators for Hamiltonian problems is introduced. This procedure is based on the combination of the trigonometric fitting technique and symplecticness conditions. Based on this procedure, a simple modified Runge–Kutta–Nyström second algebraic order trigonometrically fitted method is developed. We present explicity the symplecticity conditions for the new modified Runge–Kutta–Nyström method. Numerical results indicate that the new method is much more efficient than the "classical" symplectic Runge–Kutta–Nyström second algebraic order method introduced in Ref. 1.