Lane-Emden型方程的广义Vieta-Fibonacci多项式迭代方法  

Generalized Vieta-Fibonacci polynomial iterative method for Lane-Emden type equations

作　　者：李晓娟 蒋永新 石伟 Li Xiaojuan;Jiang Yongxin;Shi Wei(College of Science,Hohai University,Nanjing 211100,China)

机构地区：[1]河海大学理学院,江苏南京211100

出　　处：《海南大学学报（自然科学版）》2023年第3期227-238,共12页Natural Science Journal of Hainan University

基　　金：国家自然科学基金(11771207)。

摘　　要：基于广义Vieta-Fibonacci多项式的拟线性化矩阵配置方法,提出了一种求带有Dirichlet边界条件、Neumann边界条件和Neumann-Robin边界条件的一类Lane-Emden型微分方程的数值解的方法 .首先将Lane-Emden型方程拟线性化,然后利用广义Vieta-Fibonacci多项式展开得到矩阵形式,再用迭代方法进行求解.最后通过求不同边值条件下的Lane-Emden型方程的近似解,将数值结果与其他方法得到的近似解进行对比,验证了广义Vieta-Fibonacci多项式拟线性化迭代方法的有效性和准确性.In the report,a quasi-linearization matrix collocation method based on generalized Vieta-Fibonacci polynomial was proposed to solve a class of Lane-Emden differential equations with Dirichlet boundary condi-tions,Neumann boundary conditions and Neumann-Robin boundary conditions.Firstly,the Lane-Emden equa-tion was translated into a sequence of linearized equations.Secondly,the generalized Vieta-Fibonacci polynomi-al was used to expand to obtain the matrix form which is solved by the iterative method.Finally,the Lane-Em-den type equations under different boundary value conditions were solved,the numerical results were compared with that of other methods,and the accuracy and effectiveness of the generalized Vieta-Fibonacci polynomial quasi-linearization iterative method were verified.

关 键 词：Lane-Emden型方程 Vieta-Fibonacci多项式 拟线性化技术 矩阵配置方法 

分 类 号：O175[理学—数学]