NEURAL NETWORK-BASED DERIVATION OF EFFICIENT HIGH-ORDER RUNGE–KUTTA–NYSTRÖM PAIRS FOR THE INTEGRATION OF ORBITS

I. Th. Famelis ()
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I. Th. Famelis: Department of Mathematics, TEI of Athens, GR12210 Athens, Greece

International Journal of Modern Physics C (IJMPC), 2011, vol. 22, issue 12, 1309-1316

Abstract: We use a neural network approach to derive a Runge–Kutta–Nyström pair of orders 8(6) for the integration of orbital problems. We adopt a differential evolution optimization technique to choose the free parameters of the method's family. We train the method to perform optimally in a specific test orbit from the Kepler problem for a specific tolerance. Our measure of efficiency involves the global error and the number of function evaluations. Other orbital problems are solved to test the new pair.

Keywords: Runge–Kutta–Nyström; Kepler problem; neural networks; differential evolution; 02.60.Lj; 07.05.Mh (search for similar items in EconPapers)
Date: 2011
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DOI: 10.1142/S0129183111016919

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