Abstract
Recently Kilicman et al. (2006) propose a variational fixed point iteration technique with the Galerkin method for the determination of the starting function for the solution of second order linear ordinary differential equation with two-point boundary value problem without proving the convergence of the method. In this paper, a fixed point iteration method similar to Mann iteration process is proposed and successfully applied to the solution of two-point boundary value problems. We use an affine function satisfying the boundary conditions as a starting approximate solution. We also show the convergence of the method and design a Maple program for the numerical computations. Examples are given to demonstrate the agreement of the results of the proposed method with that of exact solution and existing methods.
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