Direct fifth order block method for solving second order Neumann and singular perturbed boundary value problem

This paper presents a four point block one-step method for solving directly boundary value problems (BVP) with Neumann boundary conditions and Singular Perturnbation BVPs. This method is formulated using Lagrange interpolating polynomial. The block method will solve the second order linear Neumann and Singular Perturbation BVPs directly without reducing it to the system of first order differential equations. This direct method will compute four points simultaneously within a block using constant step size. This method will be used together with linear shooting technique to construct the solutions. The implementation is based on the predictor and corrector formulas. Numerical results are given to show the efficiency of this method compared to the existing methods.