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

Authors:	Hans Van de Vyver

Institution:	^aDepartment of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200 B, B-3001 Heverlee, Belgium

Abstract:	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)} (). 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.

Keywords:	Exponential fitting Initial-value problems Oscillating solutions Orbital problems Explicit Runge–Kutta–Nyström methods Variable stepsize algorithms
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