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On a New Family of Runge–Kutta–Nyström Pairs of Orders 6(4)

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  • Vladislav N. Kovalnogov

    (Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia)

  • Ruslan V. Fedorov

    (Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia)

  • Dmitry A. Generalov

    (Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia)

  • Ekaterina V. Tsvetova

    (Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia)

  • Theodore E. Simos

    (Laboratory of Inter-Disciplinary Problems of Energy Production, Ulyanovsk State Technical University, 32 Severny Venetz Street, 432027 Ulyanovsk, Russia
    Department of Mathematics, University of Western Macedonia, GR-52100 Kastoria, Greece
    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 Deptartment, Euripus Campus, National & Kapodistrian University of Athens, GR-34400 Psachna, Greece)

Abstract

In this study, Runge–Kutta–Nyström pairs of orders 6(4) using six stages per step are considered. The main contribution of the present work is that we introduce a new family of pairs (i.e., new methodology of solution for order conditions) that possesses seven free parameters instead of four, as used by similar pairs until now. Using these extra coefficients efficiently we may construct methods with better properties. Here, we exploit the free parameters in order to derive a pair with extended imaginary stability interval. This type of method may furnish better results on problems with periodic solutions. Extended numerical tests justify our effort.

Suggested Citation

  • Vladislav N. Kovalnogov & Ruslan V. Fedorov & Dmitry A. Generalov & Ekaterina V. Tsvetova & Theodore E. Simos & Charalampos Tsitouras, 2022. "On a New Family of Runge–Kutta–Nyström Pairs of Orders 6(4)," Mathematics, MDPI, vol. 10(6), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:875-:d:767657
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    References listed on IDEAS

    as
    1. Franco, J.M. & Gómez, I., 2014. "Trigonometrically fitted nonlinear two-step methods for solving second order oscillatory IVPs," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 643-657.
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