Numerical Solutions of Sixth Order Linear and Nonlinear Boundary Value Problems

Abstract

The aim of paper is to find the numerical solutions of sixth order linear and nonlinear differential equations with two point boundary conditions. The well known Galerkin method with Bernstein and modified Legendre polynomials as basis functions is exploited. In this method, the basis functions are transformed into a new set of basis functions, which satisfy the homogeneous form of Dirichlet boundary conditions. A rigorous matrix formulation is derived for solving the sixth order BVPs. Several numerical examples are considered to verify the efficiency and implementation of the proposed method. The numerical results are compared with both the exact solutions and the results of the other methods available in the literature. The comparison shows that the performance of the present method is more efficient and yields better results.