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

Houssem Jerbi, Sondess Ben Aoun, Mohamed Omri, Theodore E. Simos and Charalampos Tsitouras
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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
Charalampos Tsitouras: General Department, National & Kapodistrian University of Athens, GR34-400 Psachna, Greece

Mathematics, 2022, vol. 10, issue 5, 1-10

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.

Keywords: initial value problem; Runge–Kutta pairs; differential evolution; periodic orbits (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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