Applied Mathematics & Information Sciences

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In this work we consider Symplectic Runge Kutta Nystr¨om methods with five stages. A new fourth algebraic order method with phase-lag order eight is presented. Also the symplectic Runge Kutta Nystr¨om of Calvo and Sanz Serna with five stages and fourth order is modified to produce a phase-fitted method. We apply the new methods on several Hamiltonian systems and on the computation of the eigenvalues of the Schr¨odinger Equation.