IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n436362.html

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

Author

Listed:
  • Abdon Atangana
  • Aden Ahmed
  • Suares Clovis Oukouomi Noutchie

Abstract

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.

Suggested Citation

  • Abdon Atangana & Aden Ahmed & Suares Clovis Oukouomi Noutchie, 2014. "On the Hamilton‐Jacobi‐Bellman Equation by the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:436362
    DOI: 10.1155/2014/436362
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/436362
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/436362?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. R. W. Beard & G. N. Saridis & J. T. Wen, 1998. "Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 589-626, March.
    2. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Abdon Atangana & Dumitru Baleanu, 2013. "Nonlinear Fractional Jaulent-Miodek and Whitham-Broer-Kaup Equations within Sumudu Transform," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, May.
    4. Abdon Atangana & Adem Kılıçman, 2013. "Analytical Solutions of Boundary Values Problem of 2D and 3D Poisson and Biharmonic Equations by Homotopy Decomposition Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chun-Guang Zhao & Ai-Min Yang & Hossein Jafari & Ahmad Haghbin, 2014. "The Yang‐Laplace Transform for Solving the IVPs with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Shun-Qin Wang & Yong-Ju Yang & Hassan Kamil Jassim, 2014. "Local Fractional Function Decomposition Method for Solving Inhomogeneous Wave Equations with Local Fractional Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    3. F. Ghomanjani & A. V. Kamyad & A. Kılıçman, 2013. "Bezier Curves Method for Fourth‐Order Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Abdon Atangana & Necdet Bildik & S. C. Oukouomi Noutchie, 2014. "New Iteration Methods for Time‐Fractional Modified Nonlinear Kawahara Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    5. Weilong You & Fu Zhang, 2025. "Pontryagin’s Principle-Based Algorithms for Optimal Control Problems of Parabolic Equations," Mathematics, MDPI, vol. 13(7), pages 1-17, March.
    6. Ali Ahmadian & Norazak Senu & Farhad Larki & Soheil Salahshour & Mohamed Suleiman & Md. Shabiul Islam, 2013. "Numerical Solution of Fuzzy Fractional Pharmacokinetics Model Arising from Drug Assimilation into the Bloodstream," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    7. Sahoo, S. & Ray, S. Saha, 2017. "Invariant analysis with conservation laws for the time fractional Drinfeld–Sokolov–Satsuma–Hirota equations," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 725-733.
    8. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    9. Milad Goodarzi & Christoph Meinerding, 2025. "Asset allocation with recursive parameter updating and macroeconomic regime identifiers," The European Journal of Finance, Taylor & Francis Journals, vol. 31(9), pages 1141-1167, June.
    10. Jinxing Liu & Muhammad Nadeem & Mustafa Habib & Shazia Karim & Harun Or Roshid, 2022. "Numerical Investigation of the Nonlinear Coupled Fractional Massive Thirring Equation Using Two‐Scale Approach," Complexity, John Wiley & Sons, vol. 2022(1).
    11. S. C. Beeler & H. T. Tran & H. T. Banks, 2000. "Feedback Control Methodologies for Nonlinear Systems," Journal of Optimization Theory and Applications, Springer, vol. 107(1), pages 1-33, October.
    12. Iqbal, Muhammad S. & Seadawy, Aly R. & Baber, Muhammad Z. & Qasim, Muhammad, 2022. "Application of modified exponential rational function method to Jaulent–Miodek system leading to exact classical solutions," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    13. Angelo Alessandri & Patrizia Bagnerini & Roberto Cianci & Mauro Gaggero, 2019. "Optimal Propagating Fronts Using Hamilton-Jacobi Equations," Mathematics, MDPI, vol. 7(11), pages 1-10, November.
    14. Morgunov, V.I. (Моргунов, В.И.), 2016. "The Liquidity Management of the Banking Sector and the Short-Term Money Market Interest Rates [Управление Ликвидностью Банковского Сектора И Краткосрочной Процентной Ставкой Денежного Рынка]," Working Papers 21311, Russian Presidential Academy of National Economy and Public Administration.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:436362. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.