Embedded Pairs of Explicit ARKN Methods for the Numerical Integration of Perturbed Oscillators

Abstract

Two new embedded pairs of explicit RKN methods specially adapted to the numerical integration of perturbed oscillators are obtained. These pairs depend upon a parameter ν = ωh>0 (h is the integration step and ω is the frequency), and they have four stages and algebraic orders four and three. The numerical experiments carried out show that the new pairs are very competitive when they are compared with a high quality code as DOPRI5.