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Journal of Applied Mathematics
Volume 2014 (2014), Article ID 654978, 13 pages
http://dx.doi.org/10.1155/2014/654978
Research Article

Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods

1Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia
2Faculty of Science & Technology, Open University Malaysia, 50603 Kuala Lumpur, Malaysia

Received 21 August 2013; Revised 9 December 2013; Accepted 16 December 2013; Published 30 January 2014

Academic Editor: Hak-Keung Lam

Copyright © 2014 Norhasimah Mahiddin and S. A. Hashim Ali. 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

The modified decomposition method (MDM) and homotopy perturbation method (HPM) are applied to obtain the approximate solution of the nonlinear model of tumour invasion and metastasis. The study highlights the significant features of the employed methods and their ability to handle nonlinear partial differential equations. The methods do not need linearization and weak nonlinearity assumptions. Although the main difference between MDM and Adomian decomposition method (ADM) is a slight variation in the definition of the initial condition, modification eliminates massive computation work. The approximate analytical solution obtained by MDM logically contains the solution obtained by HPM. It shows that HPM does not involve the Adomian polynomials when dealing with nonlinear problems.