文章基本信息

标题：Modified operational matrix method for second-order nonlinear ordinary differential equations with quadratic and cubic terms
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作者：Burcu Gürbüz ; Mehmet Sezer
期刊名称：An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
印刷版ISSN：2146-5703
出版年度：2020
卷号：10
期号：2
页码：218-225
DOI：10.11121/ijocta.01.2020.00827
出版社：An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
摘要：In this study, by means of the matrix relations between the Laguerre polynomials, and their derivatives, a novel matrix method based on collocation points is modified and developed for solving a class of second-order nonlinear ordinary differential equations having quadratic and cubic terms, via mixed conditions. The method reduces the solution of the nonlinear equation to the solution of a matrix equation corresponding to system of nonlinear algebraic equations with the unknown Laguerre coefficients. Also, some illustrative examples along with an error analysis based on residual function are included to demonstrate the validity and applicability of the proposed method.
关键词：Nonlinear ordinary differential equations;Laguerre polynomials and series;collocation points;residual error estimation