Symplectic trigonometrically fitted partitioned Runge-Kutta methods

The numerical integration of Hamiltonian systems is considered in this Letter. Trigonometrically fitted symplectic partitioned Runge-Kutta methods of second, third and fourth orders are constructed. The methods are tested on the numerical integration of the harmonic oscillator, the two body problem and an orbital problem studied by Stiefel and Bettis.