IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i15p2802-d882435.html
   My bibliography  Save this article

Multigrid Method for Solving Inverse Problems for Heat Equation

Author

Listed:
  • Hassan K. Ibrahim Al-Mahdawi

    (Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia)

  • Mostafa Abotaleb

    (Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia)

  • Hussein Alkattan

    (Department of System Programming, South Ural State University, 454080 Chelyabinsk, Russia)

  • Al-Mahdawi Zena Tareq

    (Ministry of Electricity, The State Company Electricity Production, Baghdad 10053, Iraq)

  • Amr Badr

    (Faculty of Science, School of Science and Technology, University of New England, Armidale, NSW 2350, Australia)

  • Ammar Kadi

    (Department of Food and Biotechnology, South Ural State University, 454080 Chelyabinsk, Russia)

Abstract

In this paper, the inverse problems for the boundary value and initial value in a heat equation are posed and solved. It is well known that those problems are ill posed. The problems are reformulated as integral equations of the first kind by using the separation-of-variables method. The discretization of the integral equation allowed us to reduce the integral equation to a system of linear algebraic equations or a linear operator equation of the first kind on Hilbert spaces. The Landweber-type iterative method was used in order to find an approximation solution. The V-cycle multigrid method is used to obtain more frequent and fast convergence for iteration. The numerical computation examples are presented to verify the accuracy and fast computing of the approximation solution.

Suggested Citation

  • Hassan K. Ibrahim Al-Mahdawi & Mostafa Abotaleb & Hussein Alkattan & Al-Mahdawi Zena Tareq & Amr Badr & Ammar Kadi, 2022. "Multigrid Method for Solving Inverse Problems for Heat Equation," Mathematics, MDPI, vol. 10(15), pages 1-15, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2802-:d:882435
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/15/2802/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/15/2802/
    Download Restriction: no
    ---><---

    Citations

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


    Cited by:

    1. Sergey I. Martynenko & Aleksey Yu. Varaksin, 2023. "Black-Box Solver for Numerical Simulations and Mathematical Modelling in Engineering Physics," Mathematics, MDPI, vol. 11(16), pages 1-21, August.
    2. Tao Liu & Di Ouyang & Lianjun Guo & Ruofeng Qiu & Yunfei Qi & Wu Xie & Qiang Ma & Chao Liu, 2023. "Combination of Multigrid with Constraint Data for Inverse Problem of Nonlinear Diffusion Equation," Mathematics, MDPI, vol. 11(13), pages 1-15, June.

    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:gam:jmathe:v:10:y:2022:i:15:p:2802-:d:882435. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.