Symplectic Exponentially-Fitted Modified Runge-Kutta Methods of the Gauss Type: Revisited

The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new such integrators are constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (Exponential Fitting, Kluwer Academic, Dordrecht, 2004). Numerical experiments for some oscillatory problems are presented and compared to the results obtained by previous methods.