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.