Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 917407, 23 pages
Solution of Singular and Nonsingular Initial and Boundary Value Problems
by Modified Variational Iteration Method
Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan
Received 19 May 2008; Accepted 5 June 2008
Academic Editor: Angelo Luongo
Copyright © 2008 Muhammad Aslam Noor and Syed Tauseef Mohyud-Din. 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.
We apply the modified variational iteration method (MVIM) for solving the singular
and nonsingular initial and boundary value problems in this paper. The proposed modification
is made by introducing Adomian's polynomials in the correct functional. The suggested
algorithm is quite efficient and is practically well suited for use in such problems. The proposed
iterative scheme finds the solution without any discretization, linearization, perturbation, or
restrictive assumptions. Several examples are given to verify the efficiency and reliability of
the suggested algorithm.