The Numerical Solution of Third Order Boundary Value Problems Using Piecewise Bernstein polynomials by the Galerkin Weighted Residual Method

Abstract

There are few numerical techniques available to solve third order boundary value problems. In this paper, we present Galerkin weighted residual method for constructing the numerical solution of third order linear and nonlinear boundary value problems with two point boundary conditions. The method is formulated as a rigorous matrix form. Several numerical examples of both linear and nonlinear boundary value problems in the literature are presented to illustrate the reliability and efficiency of the proposed method. The present method is quite efficient and yields better results when compared with the existing methods in the literature.

Keywords: Galerkin method, Third order linear and nonlinear BVPs, Bernstein Polynomials.