Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems


Autoria(s): GUIMARAES, Osvaldo; PIQUEIRA, Jose Roberto C.; NETTO, Marcio Lobo
Contribuinte(s)

UNIVERSIDADE DE SÃO PAULO

Data(s)

17/04/2012

17/04/2012

2011

Resumo

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.

Identificador

MATHEMATICAL PROBLEMS IN ENGINEERING, 2011

1024-123X

http://producao.usp.br/handle/BDPI/14711

10.1155/2011/521342

http://dx.doi.org/10.1155/2011/521342

Idioma(s)

eng

Publicador

HINDAWI PUBLISHING CORPORATION

Relação

Mathematical Problems in Engineering

Direitos

openAccess

Copyright HINDAWI PUBLISHING CORPORATION

Palavras-Chave #DIFFERENTIAL EVOLUTION #SCHRODINGER-EQUATION #OPERATIONAL MATRIX #NUMERICAL-SOLUTION #INTEGRATION #MODELS #Engineering, Multidisciplinary #Mathematics, Interdisciplinary Applications
Tipo

article

original article

publishedVersion