Hybrid Numerov-Type Methods with Coefficients Trained to Perform Better on Classical Orbits
Tóm tắt
This 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.
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