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

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.