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A Neural Network Type Approach for Constructing Runge–Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions

Author

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  • Houssem Jerbi

    (Department of Industrial Engineering, College of Engineering, University of Ha’il, Hail 1234, Saudi Arabia)

  • Sondess Ben Aoun

    (Department of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 1234, Saudi Arabia)

  • Mohamed Omri

    (Deanship of Scientific Research (DSR), King Abdulaziz University, Jeddah 21589, Saudi Arabia)

  • Theodore E. Simos

    (Department of Medical Research, China Medical University Hospital, China Medical University, Taichung City 40402, Taiwan
    Data Recovery Key Laboratory of Sichun Province, Neijing Normal University, Neijiang 641100, China
    Section of Mathematics, Department of Civil Engineering, Democritus University of Thrace, GR671-00 Xanthi, Greece)

  • Charalampos Tsitouras

    (General Department, National & Kapodistrian University of Athens, GR34-400 Psachna, Greece)

Abstract

We analyze a set of explicit Runge–Kutta pairs of orders six and five that share no extra properties, e.g., long intervals of periodicity or vanishing phase-lag etc. This family of pairs provides five parameters from which one can freely pick. Here, we use a Neural Network-like approach where these coefficients are trained on a couple of model periodic problems. The aim of this training is to produce a pair that furnishes best results after using certain intervals and tolerance. Then we see that this pair performs very well on a wide range of problems with periodic solutions.

Suggested Citation

  • Houssem Jerbi & Sondess Ben Aoun & Mohamed Omri & Theodore E. Simos & Charalampos Tsitouras, 2022. "A Neural Network Type Approach for Constructing Runge–Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions," Mathematics, MDPI, vol. 10(5), pages 1-10, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:5:p:827-:d:764370
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    References listed on IDEAS

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    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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    Cited by:

    1. Zacharias A. Anastassi & Athinoula A. Kosti & Mufutau Ajani Rufai, 2023. "A Parametric Method Optimised for the Solution of the (2+1)-Dimensional Nonlinear Schrödinger Equation," Mathematics, MDPI, vol. 11(3), pages 1-17, January.

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