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Neural Network-Based Derivation Of Efficient High-Order Runge–Kutta–Nyström Pairs For The Integration Of Orbits

Author

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  • I. TH. FAMELIS

    (Department of Mathematics, TEI of Athens, GR12210 Athens, Greece)

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.

Suggested Citation

  • I. Th. Famelis, 2011. "Neural Network-Based Derivation Of Efficient High-Order Runge–Kutta–Nyström Pairs For The Integration Of Orbits," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 22(12), pages 1309-1316.
    • Handle: RePEc:wsi:ijmpcx:v:22:y:2011:i:12:n:s0129183111016919
    DOI: 10.1142/S0129183111016919
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