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

Author

Listed:
  • 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
    Scientific and Educational Center “Digital Industry”, South Ural State University, 76 Lenin Ave., 454 080 Chelyabinsk, Russia
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan
    Data Recovery Key Laboratory of Sichuan Province, Neijiang Normal University, Neijiang 641100, China)

  • Charalampos Tsitouras

    (General Department, GR34-400 Euripus Campus, National & Kapodistrian University of Athens, 15772 Athens, Greece)

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.

Suggested Citation

  • Yu-Cheng Shen & Chia-Liang Lin & Theodore E. Simos & Charalampos Tsitouras, 2021. "Runge–Kutta Pairs of Orders 6(5) with Coefficients Trained to Perform Best on Classical Orbits," Mathematics, MDPI, vol. 9(12), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:12:p:1342-:d:572400
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