Abstract
We consider two step Runge-Kutta-Nyström methods for the numerical integration of y″ = f(x, y) having periodic or oscillatory solutions. We assume that the frequency ω can be estimated in advance. Using the linear stage representation, we describe how to derive two step Runge-Kutta-Nyström methods which integrate trigonometric and mixed polynomials exactly. The resulting methods depend on the parameter ν = ωh, where h is the stepsize.
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Paternoster, B. (2003). Two Step Runge-Kutta-Nyström Methods for Oscillatory Problems Based on Mixed Polynomials. In: Sloot, P.M.A., Abramson, D., Bogdanov, A.V., Gorbachev, Y.E., Dongarra, J.J., Zomaya, A.Y. (eds) Computational Science — ICCS 2003. ICCS 2003. Lecture Notes in Computer Science, vol 2658. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44862-4_15
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DOI: https://doi.org/10.1007/3-540-44862-4_15
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