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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 O(n). Furthermore, three explanatory examples established good outcomes and comparisons with exact solution

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