| Issue |
MATEC Web of Conferences
Volume 41, 2016
1st Mini Conference on Emerging Engineering Applications (MCEEA’15)
|
|
|---|---|---|
| Article Number | 05001 | |
| Number of page(s) | 4 | |
| Section | Algorithms and Applications | |
| DOI | https://doi.org/10.1051/matecconf/20164105001 | |
| Published online | 01 February 2016 | |
On the modification of Differential Evolution strategy for the construction of Runge Kutta pairs
1 TEI of Athens, Dept. of Electronic Engineering, GR12210, Athens, Greece
2 TEI of Sterea Hellas, Dept. of Automation Engineering, GR34400, Psahna Campus, Greece
a e-mail: ifamelis@teiath.gr
b e-mail: tsitouras@mail.teiste.gr
Among the most popular methods for the solution of the Initial Value Problem are the Runge–Kutta (RK) pairs. These methods can be derived by solving a system of nonlinear equations after admitting various simplifying assumptions. The more simplifying assumptions we consider the more we narrow the solution space. In [1] Tsitouras presented an algorithm for the construction of Runge–Kutta pairs of orders 5 and 4 satisfying only the so called “first column simplifying assumption”. In [2] Famelis and Tsitouras have studied the ability of Differential Evolution techniques to find solutions satisfying all the order conditions needed for the derivation of orders 5 and 4 pairs. In this work we propose an modification on the Differential Evolution strategy for the same problem. The current study will be a guide to the construction of other classes of RK that have not been presented in the literature.
© Owned by the authors, published by EDP Sciences, 2016
This is an Open Access article distributed under the terms of the Creative Commons Attribution License 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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