A trigonometrically fitted explicit hybrid method for the numerical integration of orbital problems

In this paper we present a kind of trigonometrically fitted explicit two-step hybrid method which achieves algebraic order six. The new method is zero dissipative, phase fitted, and almost P-stable. Numerical experiments from its application to well-known periodic orbital problems show that the new method is more competitive when comparing with the codes proposed by Franco [J.M. Franco, A class of explicit two-step hybrid methods for second-order IVPs, J. Comput. Appl. Math. 187 (2006) 41-57], Anastassi and Simos [Z.A. Anastassi, T.E. Simos, A trigonometrically fitted Runge-Kutta method for the numerical solution of orbital problems, New. Astron. 10 (2005) 301-309].