Closed-form solutions to differential equations via differential evolution
type: Item
instance of: scholarly article
title: Closed-form solutions to differential equations via differential evolution
zbMATH Open document ID: 1418.34039
DOI: 10.1155/2015/910316
author: L. Mex
author: Carlos A. Cruz-Villar
author: F. Peñuñuri
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: 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 optimization problem where the independent variables are \textit{elementary} functions. Second, as the domain of DE is real numbers, we propose a grammar that assigns numbers to functions. Third, to avoid truncation and subtractive cancellation errors, to increase the efficiency of the calculation of derivatives, the dual numbers are used to obtain derivatives of functions. Some examples validating the effectiveness and efficiency of our method are presented.
Mathematics Subject Classification ID: 34A45
Mathematics Subject Classification ID: 68Q05
zbMATH DE Number: 7025542
Wikidata QID: Q59105547
describes a project that uses: RKC
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/910316
OpenAlex ID: W2084208640
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description: scientific article; zbMATH DE number 7025542