Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems
Joint Authors
Piqueira, José Roberto Castilho
Lobo Netto, Marcio
Guimarães, Osvaldo
Source
Mathematical Problems in Engineering
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-26
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
This work develops a method for solving ordinary differential equations, that is, initial-value problems, with solutions approximated by using Legendre's polynomials.
An iterative procedure for the adjustment of the polynomial coefficients is developed, based on the genetic algorithm.
This procedure is applied to several examples providing comparisons between its results and the best polynomial fitting when numerical solutions by the traditional Runge-Kutta or Adams methods are available.
The resulting algorithm provides reliable solutions even if the numerical solutions are not available, that is, when the mass matrix is singular or the equation produces unstable running processes.
American Psychological Association (APA)
Guimarães, Osvaldo& Piqueira, José Roberto Castilho& Lobo Netto, Marcio. 2011. Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems. Mathematical Problems in Engineering،Vol. 2011, no. 2011, pp.1-20.
https://search.emarefa.net/detail/BIM-478335
Modern Language Association (MLA)
Guimarães, Osvaldo…[et al.]. Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems. Mathematical Problems in Engineering No. 2011 (2011), pp.1-20.
https://search.emarefa.net/detail/BIM-478335
American Medical Association (AMA)
Guimarães, Osvaldo& Piqueira, José Roberto Castilho& Lobo Netto, Marcio. Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems. Mathematical Problems in Engineering. 2011. Vol. 2011, no. 2011, pp.1-20.
https://search.emarefa.net/detail/BIM-478335
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-478335