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

Osvaldo Guimaraes; Jose Roberto C. Piqueira; Marcio Lobo Netto

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

机译：求解非线性初值问题，结合勒让德多项式和遗传算法

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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.

机译：这项工作开发了一种解决普通微分方程（即初值问题）的方法，其解决方案是使用勒让德多项式近似的。基于遗传算法，提出了多项式系数调整的迭代程序。当通过传统的Runge-Kutta或Adams方法获得数值解时，可以将该程序应用于几个示例，以提供其结果与最佳多项式拟合之间的比较。即使没有数值解，即当质量矩阵奇异或方程产生不稳定的运行过程时，生成的算法也提供了可靠的解。

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《Mathematical Problems in Engineering》 |2011年第3期|p.1-20|共20页
作者
Osvaldo Guimaraes; Jose Roberto C. Piqueira; Marcio Lobo Netto;
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Escola Politecnica da Universidade de Sao Paulo, Avenida Prof. Luciano Gualberto, travessa 3, No. 158, 05508-900 Sao Paulo, SP, Brazil;

Escola Politecnica da Universidade de Sao Paulo, Avenida Prof. Luciano Gualberto, travessa 3, No. 158, 05508-900 Sao Paulo, SP, Brazil;

Escola Politecnica da Universidade de Sao Paulo, Avenida Prof. Luciano Gualberto, travessa 3, No. 158, 05508-900 Sao Paulo, SP, Brazil;

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1. Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems [J] . OsvaldoGuimar?es, José Roberto C.Piqueira, MarcioLobo Netto Mathematical Problems in Engineering: Theory, Methods and Applications . 2011,第5期

机译：求解非线性初值问题，结合勒让德多项式和遗传算法
2. Approximate Solution of Class of Nonlinear Fractional Integro-Differential Equations Using Bernstein Polynomial and Shifted Legendre Polynomials Methods [J] . M. H. Ahmed, D. SH. Mohamed, A. K. Farhood Journal of computational and theoretical nanoscience . 2015,第12期

机译：伯恩斯坦多项式和偏移传说中的非线性分数积分微分方程类别的近似解
3. Bayesian Models combining Legendre and B-spline polynomials for genetic analysis of multiple lactations in Gyr cattle [J] . Livestock Science . 2017,第期

机译：贝叶斯模型结合了Legendre和B样条多项式的Gyr牛遗传分析
4. Hybrid solution of nonlinear stochastic optimal control problems using Legendre Pseudospectral and generalized Polynomial Chaos algorithms [C] . Frederick G. Harmon American Control Conference . 2017

机译：勒让德伪谱与广义多项式混沌算法混合的非线性随机最优控制问题
5. Hybrid solution of stochastic optimal control problems using Gauss pseudospectral method and generalized polynomial chaos algorithms. [D] . Cottrill, Gerald C. 2012

机译：使用高斯伪谱方法和广义多项式混沌算法的混合随机最优控制问题求解。
6. Analysis of Polynomial Nonlinearity Based on Measures of Nonlinearity Algorithms [O] . Mahendra Mallick, Xiaoqing Tian 2020

机译：基于非线性算法测度的多项式非线性分析
7. Combining Legendre's Polynomials and Genetic Algorithm in the Solution of Nonlinear Initial-Value Problems [O] . Osvaldo Guimarães, José Roberto C. Piqueira, Marcio Lobo Netto 2011

机译：结合Legendre多项式和遗传算法求解非线性初值问题
8. LEGENDRE, TSCHEBYSCHEFF, AND HALF-RANGE LEGENDRE POLYNOMIAL SOLUTIONS OF THE GAMMA RAY TRANSPORT EQUATION IN INFINITE HOMOGENEOUS AND TWO MEDIA PLANE GEOMETRY [R] . Burton G. Bennett, Harold L. Beck 1967

机译：无限均匀和两个媒体平面几何中的Gamma射线传输方程的LEGENDRE，TsCHEBYsCHEFF和HaLF-RaNGE LEGENDRE多项式解

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

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