IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v77y2008i4p421-435.html
   My bibliography  Save this article

Identifying the coefficient of first-order in parabolic equation from final measurement data

Author

Listed:
  • Deng, Zui-Cha
  • Yu, Jian-Ning
  • Yang, Liu

Abstract

This paper studies an inverse problem of recovering the first-order coefficient in parabolic equation when the final observation is given. Such problem has important application in a large field of applied science. The original problem is transformed into an optimal control problem by the optimization theory. The existence, uniqueness and necessary condition of the minimum for the control functional are established. By an elliptic bilateral variational inequality which is deduced from the necessary condition, an algorithm and some numerical experiments are proposed in the paper. The numerical results show that the proposed method is an accurate and stable method to determine the coefficient of first-order in the inverse parabolic problems.

Suggested Citation

  • Deng, Zui-Cha & Yu, Jian-Ning & Yang, Liu, 2008. "Identifying the coefficient of first-order in parabolic equation from final measurement data," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 421-435.
  • Handle: RePEc:eee:matcom:v:77:y:2008:i:4:p:421-435
    DOI: 10.1016/j.matcom.2008.01.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475408000086
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.matcom.2008.01.002?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lishang Jiang & Qihong Chen & Lijun Wang & Jin Zhang, 2003. "A new well-posed algorithm to recover implied local volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 451-457.
    2. Dehghan, Mehdi, 2003. "Determination of a control function in three-dimensional parabolic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 61(2), pages 89-100.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. S. Gnanavel & N. Barani Balan & K. Balachandran, 2014. "Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 992-1008, March.
    2. Yang, Liu & Dehghan, Mehdi & Yu, Jian-Ning & Luo, Guan-Wei, 2011. "Inverse problem of time-dependent heat sources numerical reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1656-1672.
    3. Yang, Liu & Deng, Zui-Cha & Yu, Jian-Ning & Luo, Guan-Wei, 2009. "Optimization method for the inverse problem of reconstructing the source term in a parabolic equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 314-326.

    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. Yishen Li & Jin Zhang, 2004. "Option pricing with Weyl-Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 457-464.
    2. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    3. Zui-Cha Deng & Y.-C. Hon & Liu Yang, 2014. "An Optimal Control Method for Nonlinear Inverse Diffusion Coefficient Problem," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 890-910, March.
    4. Gabriel TURINICI, 2008. "Local Volatility Calibration Using An Adjoint Proxy," Review of Economic and Business Studies, Alexandru Ioan Cuza University, Faculty of Economics and Business Administration, issue 2, pages 93-105, November.
    5. David Heath & Eckhard Platen, 2006. "Local volatility function models under a benchmark approach," Quantitative Finance, Taylor & Francis Journals, vol. 6(3), pages 197-206.
    6. Liang, J. & Gao, Y., 2012. "Calibration of implied volatility for the exchange rate for the Chinese Yuan from its derivatives," Economic Modelling, Elsevier, vol. 29(4), pages 1278-1285.
    7. S. Gnanavel & N. Barani Balan & K. Balachandran, 2014. "Simultaneous Identification of Two Time Independent Coefficients in a Nonlinear Phase Field System," Journal of Optimization Theory and Applications, Springer, vol. 160(3), pages 992-1008, March.
    8. Shivanian, Elyas & Jafarabadi, Ahmad, 2018. "An inverse problem of identifying the control function in two and three-dimensional parabolic equations through the spectral meshless radial point interpolation," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 82-101.
    9. Gabriel Turinici, 2009. "Calibration of local volatility using the local and implied instantaneous variance," Post-Print hal-00338114, HAL.
    10. He, Xin-Jiang & Zhu, Song-Ping, 2017. "How should a local regime-switching model be calibrated?," Journal of Economic Dynamics and Control, Elsevier, vol. 78(C), pages 149-163.
    11. Yang, Liu & Dehghan, Mehdi & Yu, Jian-Ning & Luo, Guan-Wei, 2011. "Inverse problem of time-dependent heat sources numerical reconstruction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1656-1672.
    12. Min Dai & Hanqing Jin & Xi Yang, 2024. "Data-driven Option Pricing," Papers 2401.11158, arXiv.org.
    13. Dehghan, Mehdi & Tatari, Mehdi, 2008. "Identifying an unknown function in a parabolic equation with overspecified data via He’s variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 157-166.
    14. Judith Glaser & Pascal Heider, 2012. "Arbitrage-free approximation of call price surfaces and input data risk," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 61-73, August.
    15. Yang, Liu & Deng, Zui-Cha & Yu, Jian-Ning & Luo, Guan-Wei, 2009. "Optimization method for the inverse problem of reconstructing the source term in a parabolic equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 314-326.
    16. Tatari, Mehdi & Dehghan, Mehdi, 2007. "He’s variational iteration method for computing a control parameter in a semi-linear inverse parabolic equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 671-677.
    17. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
    18. Dai, Min & Tang, Ling & Yue, Xingye, 2016. "Calibration of stochastic volatility models: A Tikhonov regularization approach," Journal of Economic Dynamics and Control, Elsevier, vol. 64(C), pages 66-81.

    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:eee:matcom:v:77:y:2008:i:4:p:421-435. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.