Construction of explicit symmetric and symplectic methods of Runge–Kutta–Nyström type for solving perturbed oscillators

The construction of explicit symmetric and symplectic methods of Runge–Kutta–Nyström (RKN) type specially adapted to the numerical solution of perturbed oscillators is analyzed. Based on the symmetry properties for this class of methods, new explicit methods of RKN type for solving perturbed oscillators are constructed. In addition, we prove that this class of explicit symmetric methods are also symplectic. 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 symmetric and symplectic methods proposed in the scientific literature for solving second-order oscillatory differential systems.