Numerical Computations of Eleventh Order Boundary Value Problems with Bezier Polynomials by Galerkin Weighted Residual Method

Abstract

Some techniques are available to solve numerically higher order boundary value problems. The aim \u00a0of this paper is to apply \u00a0Galerkin \u00a0weighted residual \u00a0method (GWRM) for solving eleventh order linear and \u00a0nonlinear \u00a0boundary \u00a0value \u00a0problems. \u00a0Using \u00a0GWRM, \u00a0approximate \u00a0solutions \u00a0of \u00a0eleventh-order \u00a0boundary value \u00a0problems \u00a0are \u00a0developed. \u00a0This \u00a0approach \u00a0provides \u00a0the \u00a0solution \u00a0in \u00a0terms \u00a0of \u00a0a \u00a0convergent \u00a0series. Approximate \u00a0results \u00a0are \u00a0given \u00a0for \u00a0several \u00a0examples \u00a0to \u00a0illustrate \u00a0the \u00a0implementation \u00a0and \u00a0accuracy \u00a0of \u00a0the method. \u00a0The \u00a0results \u00a0are \u00a0depicted \u00a0both \u00a0graphically \u00a0and \u00a0numerically. \u00a0All \u00a0results \u00a0are \u00a0compared \u00a0with \u00a0the analytical \u00a0solutions \u00a0to \u00a0show \u00a0the \u00a0convergence \u00a0of \u00a0the \u00a0proposed \u00a0algorithm. \u00a0It \u00a0is \u00a0observed \u00a0that \u00a0the \u00a0present method \u00a0is \u00a0a \u00a0more \u00a0effective \u00a0tool \u00a0and \u00a0yields \u00a0better \u00a0results. \u00a0All \u00a0problems \u00a0are \u00a0computed \u00a0using \u00a0the \u00a0software MATLAB R2017a.