Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs

Abstract

We consider the following class of three point boundary value problem $y\prime \prime (t)+f(t,y)=0$, $y\prime (0)=0,y(1)=\delta y(\eta )$, where $\delta >0$, , the source term $f(t,y)$ is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs.