Copyright © 2009 Ahmed Alsaedi and Bashir Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A generalized quasilinearization technique is developed to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of a boundary value problem involving Duffing type nonlinear integro-differential equation with integral boundary conditions. The convergence of order k (k≥2) for the sequence of iterates is also established. It is found that the work presented in this paper not only produces new results but also yields several old results in certain limits.