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

Hybrid Numerov-Type Methods with Coefficients Trained to Perform Better on Classical Orbits 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Malaysian Mathematical Sciences Society Springer Journals

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

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References (58)

Publisher
Springer Journals
Copyright
Copyright © 2019 by Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia
Subject
Mathematics; Mathematics, general; Applications of Mathematics
ISSN
0126-6705
eISSN
2180-4206
DOI
10.1007/s40840-019-00775-z
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Bulletin of the Malaysian Mathematical Sciences SocietySpringer Journals

Published: May 24, 2019

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