The general Jacobi matrix method for solving some nonlinear ordinary differential equations

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• 作者：M.R. Eslahchi^a ; ^{eslahchi@modares.ac.ir} ; Mehdi Dehghan^b ; ^{mdehghan@aut.ac.ir} ; ^{mdehghan.aut@gmail.com} ; ^{Mehdi_Dehghan@yahoo.com} ; S. Ahmadi_Asl^a ; ^{salman.ahmadiasl@modares.ac.ir}
• 关键词：Jacobi polynomials ; Matrix form ; Nonlinear differential equations ; Spectral method ; Explicit solution
• 刊名：Applied Mathematical Modelling
• 出版年：2012
• 期刊代码：6_0307904x
• 类别：cp
• 出版时间：August, 2012
• 卷：36
• 期：8
• 页码：3387-3398
• 文件大小：325 K

摘要

In this paper, we obtain the approximate solutions for some nonlinear ordinary differential equations by using the general Jacobi matrix method. Explicit formulae which express the Jacobi expansion coefficients for the powers of derivatives and moments of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. Three test problems are discussed to illustrate the efficiency of the proposed method.