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

Autor:	Houssem Jerbi, Sondess Ben Aoun, Mohamed Omri, Theodore E. Simos, Charalampos Tsitouras
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	initial value problem Runge–Kutta pairs differential evolution periodic orbits Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 5, p 827 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10050827
Popis:	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.
Databáze:	Directory of Open Access Journals
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