Numerical Approaches for Tenth and Twelfth Order Linear and Nonlinear Differential Equations

The aim of this paper is to solve the tenth and twelfth order linear and nonlinear boundary value problems numerically by the Galerkin weighted residual technique with two point boundary conditions. The well known Bernstein polynomials are exploited as basis functions in the technique and thus the basis functions are needed to modify into a new set of basis functions where the Dirichlet types of boundary conditions are satisfied. The method is developed as a rigorous matrix formulation. Numerical examples, available in the literature, are considered to implement the proposed technique. The comparison shows that the present method is more efficient and yields better results.