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 lin ear partial differential equations . Our approach consists of reducing the problem to a set of linear equations by expand ing 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 Liu Lin method . Numerical examples show better accuracy of the proposed method . Moreover , the computation cost de creases at least by a factor of 6 in this method .