A Three-Step Iterative Scheme Based on Green's Function for the Solution of Boundary Value Problems

In this manuscript, we suggest a three-step iterative scheme for finding approximate numerical solutions to boundary value problems (BVPs) in a Banach space setting. The underlying strategy of the scheme is based on embedding Green’s function into the three-step M-iterative scheme, which we will call in the paper M-Green’s iterative scheme. We assume certain possible mild conditions to prove the convergence and stability results of the suggested scheme. We also prove numerically that our M-Green iterative scheme is more effective than the corresponding Mann-Green and Khan-Green iterative schemes. Our results improve and extend some recent results in the literature of Green’s function based iteration schemes.