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 of this paper is to apply Galerkin weighted residual method (GWRM) for solving eleventh order linear and nonlinear boundary value problems. Using GWRM, approximate solutions of eleventh-order boundary value problems are developed. This approach provides the solution in terms of a convergent series. Approximate results are given for several examples to illustrate the implementation and accuracy of the method. The results are depicted both graphically and numerically. All results are compared with the analytical solutions to show the convergence of the proposed algorithm. It is observed that the present method is a more effective tool and yields better results. All problems are computed using the software MATLAB R2017a.