A Study On The Role Of Green’s Function In Solving Boundary Value Problems

ABSTRACT

The study of Green’s Functions and applications of BVPs solving different integration has been put in place in order to provide a broad understanding to the existence of Green’s Functions on solving Ordinary Differential Equations with nth order. The Green’s Functions plays an important role in solving boundary value problems of Ordinary Differential Equations. The solutions of some BVPs for linear ODEs can be denoted by its Green’s Function. Some BVPs for nonlinear Differential Equations can be transformed to nonlinear integral equations, the kernel of which are the Green’s Functions of Corresponding linear differential equations. The integral can be solved to investigate the property of the Green’s Functions. The main objective is to analyze the Green’s Function and to show how applied in solving integral equations and ODEs with the application of boundary value problems. In this paper we consider the Green’s Functions for second order linear ODEs with some Threepoint boundary conditions. As application, we study the iterative solutions for nonlinear singular second order Three-boundary value conditions, how to find Green’s Functions using a second order three-BVPs.