Numerical solutions of eighth order BVP by the Galerkin residual technique with Bernstein and Legendre polynomials

In this paper, Galerkin method with Bernstein and Legendre polynomials as basis functions is used for the numerical solutions of eighth order linear and nonlinear differential equations for two different cases of boundary conditions. In this method, the basis functions are transformed into a new set of basis functions which vanish at the boundary where the essential types of boundary conditions are defined and a matrix formulation is derived for solving the eighth order boundary value problems (BVPs). The numerical results, obtained by the proposed method, reflect that the performance of the present method is reliable, more efficient and converges monotonically to the exact solutions.