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Exponentially fitted explicit Runge-Kutta-Nyström methods. (English) Zbl 1060.65073

The author derives so-called exponentially fitted Runge-Kutta-Nyström (EFRKN) schemes to numerically solve the Cauchy problem:

y '' =f(t,y),t[t 0 ,T],y(t 0 )=y 0 ,y ' (t 0 )=y 0 ' ·

The EFRKN schemes integrate exactly differential systems whose solutions can be expressed as linear combination of the functions {exp(λt), exp(-λt)}, λ, or {sin(ωt),cos(ωt)} when λ=iω, ω. The author constructs explicit EFRKN methods with two and three stages and algebraic orders 3 an 4. He also discusses the problem of step length control and carries out numerical experiments.

65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general