Exponentially Fitted Symplectic Runge-Kutta-Nystr om methods

In this work we consider symplectic Runge Kutta Nystr öm (SRKN) methods with three stages. We construct a fourth order SRKN with constant coefficients and a trigonometrically fitted SRKN method. We apply the new methods on the two-dimentional harmonic oscillator, the Stiefel-Bettis problem and on the computation of the eigenvalues of the Schr ödinger equation.