Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 193169, 19 pages
Research Article

Existence and Analytic Approximation of Solutions of Duffing Type Nonlinear Integro-Differential Equation with Integral Boundary Conditions

Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 16 November 2008; Accepted 14 January 2009

Academic Editor: Yong Zhou

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.


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(k2) 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.