Eighth Order Two-Step Methods Trained to Perform Better on Keplerian-Type Orbits

Vladislav N. Kovalnogov, Ruslan V. Fedorov, Andrey V. Chukalin, Theodore E. Simos and Charalampos Tsitouras
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Vladislav N. Kovalnogov: Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 432027 Ulyanovsk, Russia
Ruslan V. Fedorov: Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 432027 Ulyanovsk, Russia
Andrey V. Chukalin: Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 432027 Ulyanovsk, Russia
Theodore E. Simos: Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 432027 Ulyanovsk, Russia
Charalampos Tsitouras: General Department, National & Kapodistrian University of Athens, 10679 Athens, Greece

Mathematics, 2021, vol. 9, issue 23, 1-19

Abstract: The family of Numerov-type methods that effectively uses seven stages per step is considered. All the coefficients of the methods belonging to this family can be expressed analytically with respect to four free parameters. These coefficients are trained through a differential evolution technique in order to perform best in a wide range of Keplerian-type orbits. Then it is observed with extended numerical tests that a certain method behaves extremely well in a variety of orbits (e.g., Kepler, perturbed Kepler, Arenstorf, Pleiades) for various steplengths used by the methods and for various intervals of integration.

Keywords: initial value problem (IVP; second-order IVP); Numerov-type methods; two-body problem; perturbed Kepler; differential evolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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