An Iterative Approach for the Numerical Solution of Fractional BVPs

Abstract

In this article, an efficient numerical scheme is presented for the numerical solution of nonlinear multi-point boundary value problems. This method is a combination of Laplace transform and a decomposition procedure, commonly known as the Laplace Decomposition Method. This semi-analytical iterative scheme is highly accurate locally as it produces series solutions, which converges over a relatively short interval. In order to demonstrate the efficiency and simplicity of the method, the proposed strategy is implemented for a number of boundary value problems of fractional order. Comparisons with other existing techniques are reported. Few iterates of this iterative scheme are needed to obtain highly accurate solution, which indicates that the rate of convergence of the scheme is relatively high.