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An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions. (English) Zbl 1001.65080
Summary: An exponentially-fitted Runge-Kutta method for the numerical integration of initial-value problems with periodic or oscillating solutions is developed. Numerical and theoretical results obtained for several well known problems show the efficiency of the new method.

MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L05Initial value problems for ODE (numerical methods)
34C10Qualitative theory of oscillations of ODE: zeros, disconjugacy and comparison theory
34A34Nonlinear ODE and systems, general
34C25Periodic solutions of ODE
70M20Orbital mechanics (general mechanics)