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- Title
A Neural Network Type Approach for Constructing Runge–Kutta Pairs of Orders Six and Five That Perform Best on Problems with Oscillatory Solutions.
- Authors
Jerbi, Houssem; Ben Aoun, Sondess; Omri, Mohamed; Simos, Theodore E.; Tsitouras, Charalampos
- 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.
- Subjects
INITIAL value problems; DIFFERENTIAL evolution
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 5, p827
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10050827