Exponentially fitted explicit Runge-Kutta-Nyström methods

Authors:
J. M. Franco
Affiliations:
Departamento de Matemática Aplicada, C.P.S. de Ingeniería, Universidad de Zaragoza, María de Luna 3, 50018 Zaragoza, Spain
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

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Abstract

Exponentially fitted Runge-Kutta-Nyström (EFRKN) methods for the numerical integration of second-order IVPs with oscillatory solutions are derived. These methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(λt), exp(-λt)}, λ ∈ C, or equivalently {sin(ωt), cos(ωt)} when λ = iω, ω ∈ R. Explicit EFRKN methods with two and three stages and algebraic orders 3 and 4 are constructed. In addition, a 4(3) embedded pair of explicit EFRKN methods based on the FSAL technique is obtained, which permits to introduce an error and step length control with a small cost added. Some numerical experiments show the efficiency of our explicit EFRKN methods when they are compared with other exponential fitting type codes proposed in the scientific literature.