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Abstract and Applied Analysis
Volume 2013, Article ID 380484, 9 pages
Research Article

Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics and Institute for Mathematical Research, University of Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 13 June 2013; Accepted 18 August 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Abdon Atangana and Adem Kılıçman. 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.


The homotopy decomposition method, a relatively new analytical method, is used to solve the 2D and 3D Poisson equations and biharmonic equations. The method is chosen because it does not require the linearization or assumptions of weak nonlinearity, the solutions are generated in the form of general solution, and it is more realistic compared to the method of simplifying the physical problems. The method does not require any corrected function or any Lagrange multiplier and it avoids repeated terms in the series solutions compared to the existing decomposition method including the variational iteration method, the Adomian decomposition method, and Homotopy perturbation method. The approximated solutions obtained converge to the exact solution as tends to infinity.