Closed-Form Solutions to Differential Equations via Differential Evolution
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 optim...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2015-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2015/910316 |
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| 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 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. |
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| ISSN: | 1026-0226 1607-887X |