On the solutions of three-point boundary value problems using variational-fixed point iteration method

Given a three-point fourth-order boundary value problems yðivÞ þ pðxÞy000 þ qðxÞy00 þ rðxÞy0 þ sðxÞy ¼ fðxÞ; a x b such that yðaÞ ¼ yðbÞ ¼ y00ðbÞ ¼ y00ðaÞ 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.