An Efficient Iterative Method for Nonlinear Boundary Value Problems with Existence and Uniqueness

Abstract

A simple and efficient iterative method involving Green’s function is presented for solving the general [Formula: see text]th-order nonlinear boundary value problems. Existence and uniqueness results for such problems are established using the fixed-point theorems. This guarantees the uniform convergence of the proposed iterative algorithm. The resulting iterative solutions does not contain any unknown constants and automatically satisfy the given boundary conditions. This gives the iterative method much wider applicability in obtaining the analytical or numerical solution of the problem. The performance of the proposed approach is assessed and tested on four examples.