An exponentially-fitted high order method for long-term integration of periodic initial-value problems Original Research Article

In this paper an exponentially-fitted eighth algebraic order explicit symmetric method is developed. The new method integrates exactly any linear combination of the functions {1,x,x2,x3,x4,x5,x6,x7,exp(±wx)}. Numerical results on long term integration of well-known periodic problems indicate that the new method is much more efficient than the “classical” symmetric eighth algebraic order developed by Quinlan and Tremaine [Astronom. J. 100 (1990) 1694–1700] and the well-known Runge–Kutta–Nyström Dormand et al. eighth algebraic order method [IMA J. Numer. Anal. 7(1987) 423–430].