An Exponentially Fitted 6(4) Pair of Explicit Runge-Kutta-Nystroem Methods

摘要

In this work we construct an ebbedded pair of exponentially fitted Runge-Kutta-Nystrom methods. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions exp(wx)methods, exp(-wx), w ∈R or w ∈ iR. We modify the pair of six and fourth order formulae suggested in [1] (RKN6(4)6FM). We apply the new method on the integration of orbital problems such as the two body problem and an orbit problem studied by Steifel and Bettis.