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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 436362, 8 pages
Research Article

On the Hamilton-Jacobi-Bellman Equation by the Homotopy Perturbation Method

1Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa
2Department of Mathematics, Texas A&M University, MSC 172, 700 University Boulevard, Kingsville, TX, USA
3Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa

Received 16 April 2014; Revised 24 May 2014; Accepted 1 June 2014; Published 22 June 2014

Academic Editor: Guo-Cheng Wu

Copyright © 2014 Abdon Atangana 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.


Our concern in this paper is to use the homotopy decomposition method to solve the Hamilton-Jacobi-Bellman equation (HJB). The approach is obviously extremely well organized and is an influential procedure in obtaining the solutions of the equations. We portrayed particular compensations that this technique has over the prevailing approaches. We presented that the complexity of the homotopy decomposition method is of order . Furthermore, three explanatory examples established good outcomes and comparisons with exact solution.