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

Abstract

The \u00a0aim \u00a0of \u00a0this \u00a0paper \u00a0is \u00a0to \u00a0apply \u00a0Galerkin \u00a0weighted \u00a0residual \u00a0method \u00a0for \u00a0solving \u00a0tenth \u00a0and twelfth \u00a0order \u00a0linear \u00a0and \u00a0nonlinear \u00a0boundary \u00a0value \u00a0problems \u00a0(BVPs). \u00a0A \u00a0trial \u00a0function \u00a0is \u00a0assumed \u00a0which \u00a0is made \u00a0to \u00a0satisfy \u00a0the \u00a0boundary \u00a0conditions \u00a0given, \u00a0and \u00a0used \u00a0to \u00a0generate \u00a0the \u00a0residual \u00a0to \u00a0be \u00a0minimized. \u00a0The method \u00a0is \u00a0formulated \u00a0as \u00a0a rigorous matrix form. \u00a0To \u00a0investigate \u00a0the \u00a0effectiveness of \u00a0the method, \u00a0numerical 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. \u00a0