Journal of Applied Mathematics
Volume 2013 (2013), Article ID 392567, 10 pages
http://dx.doi.org/10.1155/2013/392567
Research Article

Fractional Variational Iteration Method versus Adomian’s Decomposition Method in Some Fractional Partial Differential Equations

Junqiang Song,1 Fukang Yin,1 Xiaoqun Cao,1 and Fengshun Lu2

1College of Computer, National University of Defense Technology, Changsha, Hunan 410073, China
2China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China

Received 17 September 2012; Revised 28 December 2012; Accepted 31 December 2012

Academic Editor: Zhongxiao Jia

Copyright © 2013 Junqiang Song et al. 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 comparative study is presented about the Adomian’s decomposition method (ADM), variational iteration method (VIM), and fractional variational iteration method (FVIM) in dealing with fractional partial differential equations (FPDEs). The study outlines the significant features of the ADM and FVIM methods. It is found that FVIM is identical to ADM in certain scenarios. Numerical results from three examples demonstrate that FVIM has similar efficiency, convenience, and accuracy like ADM. Moreover, the approximate series are also part of the exact solution while not requiring the evaluation of the Adomian’s polynomials.