Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems
Contribuinte(s) |
UNIVERSIDADE DE SÃO PAULO |
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Data(s) |
17/04/2012
17/04/2012
2011
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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 |
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 |