On fitted modifications of Runge–Kutta–Nyström pairs

Modification of only four coefficients of the standard Runge–Kutta–Nyström pairs is enough for producing a method of the same orders that integrates exactly the harmonic oscillator as model problem. These new coefficients are O(λ2)O(λ2) perturbations of the initial ones, with λλ the frequency of the problem. Theoretical investigation for the possibilities of order reduction is given. Numerical results over standard pairs of orders 6(4) and 8(6) justify our efforts.