A Note on Existence Results for a Class of Three-Point Nonlinear BVPs

Abstract

This article deals with a computational iterative technique for the following second order three point boundary value problem

y''(t) + f(t, y, y' ) = 0, 0 < t < 1,

y(0) = 0, y(1) = δy(η),

where f(I × R, R), I = [0, 1], 0 < η < 1, δ > 0. We consider simple iterative scheme and develop a monotone iterative technique. Some examples are constructed to show the accuracy of the present method. We show that our technique is quite powerful and some user friendly packages can be developed by using this technique to compute the solutions of the nonlinear three point BVPs whose close form solutions are not known.

Keyword : nonlinear boundary value problems, Green’s function, three point BVP, monotone iterative technique, upper and lower solutions