Given a three-point fourth-order boundary value problems y ðivÞ þ pðxÞy 000 þ qðxÞy 00 þ rðxÞy 0 þ sðxÞy ¼ f ðxÞ; a x b such that yðaÞ ¼ yðbÞ ¼ y 00 ðbÞ ¼ y 00 ðaÞ ¼ 0; a a b; where p; q; r; s; f 2 C½a; b , we combine the application of variational iteration method and fixed point iteration process to construct an iterative scheme called variationalfixed point iteration method that approximates the solution of three-point boundary value problems. The success of the variational or weighted residual method of approximation from a practical point of view depends on the suitable selection of the basis function. The method is self correcting one and leads to fast convergence. Problems were experimented to show the effectiveness and accuracy of the proposed method.Keywords Fixed point iteration Á Variational iteration method Á Lagrange's multiplier and boundary value problems.

In this paper, we propose a variational-fixed point iteration technique for the solution of second order linear differential equations with two-point boundary value problems. The proposed method is endowed with the Galerkin method for the determination of the starting function. The numerical results show the validity and efficiency of the proposed method in comparison withthe exact solution and other existing methods.