IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2012y2012i1n390876.html

Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation

Author

Listed:
  • Xiuming Li
  • Suping Qian

Abstract

This paper investigates the inverse problem of determining a heat source in the parabolic heat equation using the usual conditions. Firstly, the problem is reduced to an equivalent problem which is easy to handle using variational iteration method. Secondly, variational iteration method is used to solve the reduced problem. Using this method a rapid convergent sequence can be produced which tends to the exact solution of the problem. Furthermore, variational iteration method does not require the discretization of the problem. Two numerical examples are presented to illustrate the strength of the method.

Suggested Citation

  • Xiuming Li & Suping Qian, 2012. "Numerical Solution of the Inverse Problem of Determining an Unknown Source Term in a Heat Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:390876
    DOI: 10.1155/2012/390876
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2012/390876
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2012/390876?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. Wazwaz, Abdul-Majid, 2008. "A study on linear and nonlinear Schrodinger equations by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1136-1142.
    2. Dehghan, Mehdi & Saadatmandi, Abbas, 2009. "Variational iteration method for solving the wave equation subject to an integral conservation condition," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1448-1453.
    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. Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
    2. Mrutyunjaya Sahoo & Snehashish Chakraverty, 2022. "Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment," Mathematics, MDPI, vol. 10(16), pages 1-24, August.
    3. Chein-Shan Liu & Chih-Wen Chang & Yung-Wei Chen & Jian-Hung Shen, 2022. "To Solve Forward and Backward Nonlocal Wave Problems with Pascal Bases Automatically Satisfying the Specified Conditions," Mathematics, MDPI, vol. 10(17), pages 1-16, August.
    4. Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "Efficacy of variational iteration method for chaotic Genesio system – Classical and multistage approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2152-2159.
    5. Aydın, Ayhan, 2009. "Multisymplectic integration of N-coupled nonlinear Schrödinger equation with destabilized periodic wave solutions," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 735-751.
    6. Yukun Zhao & Yujie Chen & Jun Dai & Ying Wang & Wei Wang, 2019. "Bright Soliton Solution of (1+1)‐Dimensional Quantum System with Power‐Law Dependent Nonlinearity," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
    7. Ravi Kanth, A.S.V. & Aruna, K., 2009. "Two-dimensional differential transform method for solving linear and non-linear Schrödinger equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2277-2281.
    8. Younghae Do & Bongsoo Jang, 2012. "Nonlinear Klein‐Gordon and Schrödinger Equations by the Projected Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    9. Rizvi, Syed T.R. & Seadawy, Aly R. & Ahmed, Sarfaraz & Younis, Muhammad & Ali, Kashif, 2021. "Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    10. Liu, Chein-Shan & Chen, Yung-Wei & Shen, Jian-Hung & Chang, Yen-Shen, 2025. "Solving higher-order nonlocal boundary value problems with high precision by the fixed quasi Newton methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 232(C), pages 211-226.
    11. Ulutas, Esma, 2021. "Travelling wave and optical soliton solutions of the Wick-type stochastic NLSE with conformable derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).

    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:jnljam:v:2012:y:2012:i:1:n:390876. 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/4185 .

    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.