New Implementation of Legendre Polynomials for Solving Partial Differential Equations

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.

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Davari, A. and Ahmadi, A. (2013) New Implementation of Legendre Polynomials for Solving Partial Differential Equations. Applied Mathematics, 4, 1647-1650. doi: 10.4236/am.2013.412224.

Conflicts of Interest

The authors declare no conflicts of interest.

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