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Mohammadi, A., Manteghian, M. and Mohammadi, A. (2011) Numerical Solution of the One-Dimensional Advection-Diffusion Equation Using Simultaneously Temporal and Spatial Weighted Parameters. Australian Journal of Basic and Applied Sciences, 5, 1536-1543.

has been cited by the following article:

• TITLE: Discontinuous Legendre Wavelet Galerkin Method for One-Dimensional Advection-Diffusion Equation

  AUTHORS: Xiaoyang Zheng, Zhengyuan Wei

  KEYWORDS: Advection-Diffusion Equation, Legendre Wavelet, Discontinuous Galerkin Method, Discontinuous Legendre Wavelet Galerkin Method

  JOURNAL NAME: Applied Mathematics, Vol.6 No.9, August 21, 2015

  ABSTRACT: This paper presents discontinuous Legendre wavelet Galerkin (DLWG) approach for solving one-dimensional advection-diffusion equation (ADE). Variational formulation of this type equation and corresponding numerical fluxes are devised by utilizing the advantages of both the Legendre wavelet bases and discontinuous Galerkin (DG) method. The distinctive features of the proposed method are its simple applicability for a variety of boundary conditions and able to effectively approximate the solution of PDEs with less storage space and execution. The results of a numerical experiment are provided to verify the efficiency of the designed new technique.