An optimized sixth-order explicit RKN method to solve oscillating systems

Abstract

Optimization of the sixth-order explicit Runge-Kutta-Nyström method with six stages derived by El-Mikkawy and Rahmo using the phase-fitted and amplification-fitted techniques with constant step-size is developed in this paper. The new method integrates exactly the common test: 𝑦00 = −𝑤2𝑦. The local truncation error of the new method is computed, showing that the order of convergence is maintained. The stability analysis is addressed, showing that the developed method has a periodicity interval. The numerical experiments demonstrate the high performance of the proposed scheme compared to other existing RKN codes with six stages and same order.