A Novel Numerical Approach for Odd Higher Order Boundary Value Problems

Abstract

In this paper, we investigate numerical solutions of odd higher order differential equations, particularly the fifth, seventh and ninth order linear and nonlinear boundary value problems (BVPs) with two point boundary conditions.  We exploit Galerkin weighted residual method with Legendre polynomials as basis functions. Special care has been taken to satisfy the corresponding homogeneous form of boundary conditions where the essential types of boundary conditions are given. The method is formulated as a rigorous matrix form. Several numerical examples, of both linear and nonlinear BVPs available 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.

Keywords: Galerkin method, fifth, seventh and ninth order linear and nonlinear BVPs, Legendre Polynomials.