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Hybrid Numerov-Type Methods with Coefficients Trained to Perform Better on Classical Orbits

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AbstractThis manuscript constructed a class of explicit hybrid Numerov methods of sixth order for second-order ordinary differential equations. The methods have four stages at each step with coefficients expressed explicitly… Click to show full abstract

AbstractThis manuscript constructed a class of explicit hybrid Numerov methods of sixth order for second-order ordinary differential equations. The methods have four stages at each step with coefficients expressed explicitly with respect to a couple of free parameters. The coefficients are “trained” so that the methods perform best on a single Kepler orbit. In the experiment, the new methods outperform the ones in the literature for various eccentricities, costs and time intervals.

Keywords: coefficients trained; trained perform; methods coefficients; numerov type; hybrid numerov; type methods

Journal Title: Bulletin of the Malaysian Mathematical Sciences Society
Year Published: 2019

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