Symplectic explicit methods of Runge–Kutta–Nyström type for solving perturbed oscillators

The construction of symplectic methods of Runge–Kutta–Nyström type (RKN-type) specially adapted to the numerical solution of perturbed oscillators is analyzed. Based on the symplecticity conditions for this class of methods, new fourth-order explicit methods of RKN type for solving perturbed oscillators are constructed. The derivation of the new symplectic methods is carried out paying special attention to the minimization of the principal term of the local truncation error. The numerical experiments carried out show the qualitative behavior and the efficiency of the new methods when they are compared with some standard and specially adapted symplectic methods proposed in the scientific literature for solving second-order oscillatory differential systems.