Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

Discontinuous Legendre Wavelet Galerkin Method for Solving Lane-Emden Type Equation

Download PDF (611.5 KB) PP. 29 - 43 Pub. Date: January 1, 2016

DOI: 10.22606/jaam.2016.11004


  • Xiaoyang Zheng*
    College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China
  • Zhengyuan Wei
    College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China
  • Jiangping He
    College of Mathematics and Statistics, Chongqing University of Technology, 400054, Chongqing, China


This paper presents a new numerical approach, i.e., discontinuous Legendre wavelet Galerkin (DLWG) technique, to solve the Lane-Emden equations. This scheme incorporates Legendre wavelet into discontinuous Galerkin (DG) method, thus it has the advantages of both wavelet Galerkin (WG) method and DG technique. Specifically, the variational formulation of the equation and numerical fluxes are first derived and clearly calculated, then the Lane-Emden equations are converted into solutions to systems of equations. It is pointed that the proposed approach needs less storage space and execution time than the other methods because of the use of discontinuous elements producing lower dimensional, block-diagonal and sparse mass matrices. Furthermore, numerical experiments demonstrate the efficiency and applicability of this technique.


Legendre wavelet, Discontinuous Galerkin method, Lane-Emden equation, Discontinuous Legendre wavelet Galerkin method.


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