Runge–Kutta Pairs of Orders 6(5) with Coefficients Trained to Perform Best on Classical Orbits

Yu-Cheng Shen, Chia-Liang Lin, Theodore E. Simos and Charalampos Tsitouras
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Yu-Cheng Shen: Department of Preschool Education, School of Educational Sciences, Huaiyin Campus, Huaiyin Normal University, Huaian City 223300, China
Chia-Liang Lin: Department of Visual Communications, School of Arts, Huzhou University, Huzhou 313000, China
Theodore E. Simos: College of Applied Mathematics, Chengdu University of Information Technology, Chengdu 610225, China
Charalampos Tsitouras: General Department, GR34-400 Euripus Campus, National & Kapodistrian University of Athens, 15772 Athens, Greece

Mathematics, 2021, vol. 9, issue 12, 1-9

Abstract: We consider a family of explicit Runge–Kutta pairs of orders six and five without any additional property (reduced truncation errors, Hamiltonian preservation, symplecticness, etc.). This family offers five parameters that someone chooses freely. Then, we train them in order for the presented method to furnish the best results on a couple of Kepler orbits, a certain interval and tolerance. Consequently, we observe an efficient performance on a wide range of orbital problems (i.e., Kepler for a variety of eccentricities, perturbed Kepler with various disturbances, Arenstorf and Pleiades). About 1.8 digits of accuracy is gained on average over conventional pairs, which is truly remarkable for methods coming from the same family and order.

Keywords: initial value problem; Kepler-type orbits; Runge–Kutta; differential evolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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