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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

  • 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.

     

    Abstract: 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 conditions, Neumann boundary conditions and Neumann-Robin boundary conditions. Firstly, the Lane-Emden equation was translated into a sequence of linearized equations. Secondly, the generalized Vieta-Fibonacci polynomial was used to expand to obtain the matrix form which is solved by the iterative method. Finally, the Lane-Emden 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.

     

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