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Closed-Form Solutions to Differential Equations via Differential Evolution
Joint Authors
Mex, L.
Cruz-Villar, Carlos A.
Peñuñuri, F.
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-03-11
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We focus on solving ordinary differential equations using the evolutionary algorithm known as differential evolution (DE).
The main purpose is to obtain a closed-form solution to differential equations.
To solve the problem at hand, three steps are proposed.
First, the problem is stated as an optimizationproblem where the independent variables are elementary functions.
Second, as the domain of DE isreal numbers, we propose a grammar that assigns numbers to functions.
Third, to avoid truncationand subtractive cancellation errors, to increase the efficiency of the calculation of derivatives, the dualnumbers are used to obtain derivatives of functions.
Some examples validating the effectiveness andefficiency of our method are presented.
American Psychological Association (APA)
Mex, L.& Cruz-Villar, Carlos A.& Peñuñuri, F.. 2015. Closed-Form Solutions to Differential Equations via Differential Evolution. Discrete Dynamics in Nature and Society،Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1060811
Modern Language Association (MLA)
Mex, L.…[et al.]. Closed-Form Solutions to Differential Equations via Differential Evolution. Discrete Dynamics in Nature and Society No. 2015 (2015), pp.1-11.
https://search.emarefa.net/detail/BIM-1060811
American Medical Association (AMA)
Mex, L.& Cruz-Villar, Carlos A.& Peñuñuri, F.. Closed-Form Solutions to Differential Equations via Differential Evolution. Discrete Dynamics in Nature and Society. 2015. Vol. 2015, no. 2015, pp.1-11.
https://search.emarefa.net/detail/BIM-1060811
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1060811