On fitted modifications of Runge–Kutta–Nyström pairs

摘要

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) perturbations of the initial ones, with λ 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.