论文信息 - Exponentially fitted explicit Runge-Kutta-Nyström methods

Exponentially fitted explicit Runge-Kutta-Nyström methods

Exponentially fitted Runge-Kutta-Nystrom (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.

J. M. Franco

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