An embedded exponentially fitted Runge–Kutta–Nyström method for the numerical solution of orbital problems

A new embedded pair of explicit exponentially fitted Runge–Kutta–Nyström methods is constructed. The methods integrate exactly systems of differential equations whose solutions are linear combinations of the functions from the set {exp(μt), exp(−μt  )} (μ∈Rorμ∈iR). The pair has four stages and algebraic orders five and three. An application to some well-known orbital problem shows that the new pair is very competitive when it is compared with high-quality codes proposed in the scientific literature.