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.
Kalogiratou, Z.; Monovasilis, Th.; and E. Simos, T.
"Symplectic Runge-Kutta-Nystr?m Methods with Phase-Lag Oder 8 and Infinity,"
Applied Mathematics & Information Sciences: Vol. 09:
3, Article 2.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss3/2