Abstract
A new implicit Runge-Kutta-Nyström method with variable coefficients is developed for solving the periodic initial value problem of the differential equationy″ = f(t,y). The proposed method, whose coefficients are functions of the frequency and the stepsize, integrates exactly the equation, if the solution is a periodic function with a single Fourier component and the frequency is known. On the other hand, the order of accuracy of the method is shown to be 4 for the case that an estimated frequency, instead of the exact one, is applied to evaluate the coefficients, as well as for that the solution is non-periodic.
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Ozawa, K. A four-stage implicit Runge-Kutta-Nyström method with variable coefficients for solving periodic initial value problems. Japan J. Indust. Appl. Math. 16, 25 (1999). https://doi.org/10.1007/BF03167523
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DOI: https://doi.org/10.1007/BF03167523