A New Phase- and Amplification-Fitted Sixth-Order Explicit RKN Method to Solve Oscillating Systems

Musa Ahmed Demba, Higinio Ramos, Wiboonsak Watthayu, Idris Ahmed

Abstract

An optimization of the sixth-order explicit Runge-Kutta-Nystr\"{o}m  method with six stages derived by El-Mikkawy and Rahmo using the phase-fitted and amplification-fitted techniques with constant step-size is constructed in this paper. The new adapted method integrates exactly the common test: $y^{\prime \prime}=-w^{2}y$. 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 is "almost" P-stable. The numerical experiments demonstrate the high performance of the proposed scheme compared to other existing explicit RKN codes with six stages and same order.