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.
Highlights
There are several applications of partial differential equations (PDEs) in science and engineering [1,2]
Orthogonal functions and polynomials have been employed by many authors for solving various PDEs
The main idea is using an orthogonal basis to reduce the problem under study to a system of linear algebraic equations
Summary
There are several applications of partial differential equations (PDEs) in science and engineering [1,2]. Analytical solution of PDEs, either does not exist or is difficult to find Recent contribution in this regard includes meshless methods [3], finite-difference methods [4], Alternating-Direction Sinc-Galerkin method (ADSG) [5], quadratic spline collocation method (QSCM) [6], Liu and Lin method [7] and so on. Orthogonal functions and polynomials have been employed by many authors for solving various PDEs. The main idea is using an orthogonal basis to reduce the problem under study to a system of linear algebraic equations. We have applied a method based on Legendre polynomials basis on the unit square. This method is simple to understand and easy to implement using computer packages and yields better results.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
