Bezier Polynomials and its Applications with the Tenth and Twelfth Order Boundary Value Problems

Abstract

The aim of this paper is to apply Galerkin weighted residual method for solving tenth and twelfth order linear and nonlinear boundary value problems (BVPs). A trial function is assumed which is made to satisfy the boundary conditions given, and used to generate the residual to be minimized. The method is formulated as a rigorous matrix form. To investigate the effectiveness of the method, numerical examples were considered which were compared with both the analytic solutions and the solutions obtained by our method. It is observed that, the proposed method is very accurate, better, efficient and appropriate. All problems are computed using the software MATLAB.