A 6(4) optimized embedded Runge–Kutta–Nyström pair for the numerical solution of periodic problems

In this paper an optimization of the non-FSAL embedded RKN 6(4)6(4) pair with six stages of Moawwad El-Mikkawy, El-Desouky Rahmo is presented. The new method is derived after applying phase-fitting and amplification-fitting and has variable coefficients. The preservation of the algebraic order is verified and the principal term of the local truncation error is evaluated. Furthermore, periodicity analysis is performed, which reveals that the new method is “almost” P-stable. The efficiency of the new method is measured via the integration of several initial value problems.