A modified fixed point iterative scheme based on Green’s function with application to BVPs

Abstract

This paper presents a new faster iteration approach that is based upon the well-known three-step fixed point iteration scheme called SP-iterative scheme for a broad and larger class of non-linear BVPs. The scheme is constructed using Green’s function based integral operator and the new modified scheme in the paper will be called SP–Green’s iterative scheme. We present a fixed point convergence theorem using some assumption on the sequences of scalars in our scheme. We also prove the weak [Formula: see text]-stability for our scheme and present a numerical example to support our scheme. We provide eventually applications of our scheme to a second-order BVP and a singular BVP of isothermal gas sphere.