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

Osvaldo Guimarães | Zendy; José Roberto Castilho Piqueira | Zendy; Márcio Lobo Netto | Zendy

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

Author(s) -

Osvaldo Guimarães,

José Roberto Castilho Piqueira,

Márcio Lobo Netto

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/521342

Subject(s) - legendre polynomials , mathematics , associated legendre polynomials , nonlinear system , value (mathematics) , genetic algorithm , algorithm , classical orthogonal polynomials , orthogonal polynomials , mathematical optimization , gegenbauer polynomials , pure mathematics , mathematical analysis , physics , statistics , quantum mechanics

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

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