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has been cited by the following article:

• TITLE: New Implementation of Legendre Polynomials for Solving Partial Differential Equations

  AUTHORS: Ali Davari, Abozar Ahmadi

  KEYWORDS: Legendre Polynomials; Partial Differential Equations; Collocation Method

  JOURNAL NAME: Applied Mathematics, Vol.4 No.12, December 3, 2013

  ABSTRACT: In this paper we present a proposal using Legendre polynomials approximation for the solution of the second order linear partial differential equations. Our approach consists of reducing the problem to a set of linear equations by expanding the approximate solution in terms of shifted Legendre polynomials with unknown coefficients. The performance of presented method has been compared with other methods, namely Sinc-Galerkin, quadratic spline collocation and LiuLin method. Numerical examples show better accuracy of the proposed method. Moreover, the computation cost decreases at least by a factor of 6 in this method.