A Phase-Fitted and Amplification-Fitted Explicit Runge–Kutta–Nyström Pair for Oscillating Systems

An optimized embedded 5(3) pair of explicit Runge–Kutta–Nyström methods with four stages using phase-fitted and amplification-fitted techniques is developed in this paper. The new adapted can exactly integrate (except round-off errors) the common test: y?=?w2y. local truncation error method derived, we show that order convergence maintained. stability analysis addressed, demonstrate absolutely stable, thus appropriate for solving stiff problems. numerical experiments a better performance comparison other existing RKN pairs similar characteristics.