An improvement to the homotopy perturbation method for solving the Hamilton-Jacobi-Bellman equation

@article{Effati2013AnIT,
  title={An improvement to the homotopy perturbation method for solving the Hamilton-Jacobi-Bellman equation},
  author={Sohrab Effati and Hassan Saberi Nik and Mohammad Shirazian},
  journal={IMA J. Math. Control. Inf.},
  year={2013},
  volume={30},
  pages={487-506}
}
In this paper, the piecewise homotopy perturbation method (PHPM) is employed to solve the Hamilton– Jacobi–Bellman (HJB) equation arising in the optimal control problems. The method is a simple modification of the standard homotopy perturbation method (HPM), in which it is treated as an algorithm in a sequence of small intervals (i.e. time step) for finding accurate approximate solutions to the corresponding HJB equation. Applying the PHPM with He’s polynomials reveals that the modified… 
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