IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v386y2020ics0096300320304744.html
   My bibliography  Save this article

Gradient preserved method for solving heat conduction equation with variable coefficients in double layers

Author

Listed:
  • Bora, Aniruddha
  • Dai, Weizhong

Abstract

Recently, we have developed an accurate compact finite difference scheme called the Gradient Preserved Method (GPM) for solving heat conduction equation with constant coefficients in double layers. Since functionally graded materials are becoming paramount than materials having uniform structures with the development of new materials, this article extends the GPM to the case where coefficients are variable (and even temperature-dependent). The higher-order compact finite scheme is obtained based on three grid points and is proved to be unconditionally stable and convergent with O(τ2+h4), where τ and h are the time step and grid size, respectively. Numerical errors and convergence orders are tested in an example. Finally, we apply the scheme for predicting electron and lattice temperatures of a gold thin film padding on a chromium film exposed to the ultrashort-pulsed laser.

Suggested Citation

  • Bora, Aniruddha & Dai, Weizhong, 2020. "Gradient preserved method for solving heat conduction equation with variable coefficients in double layers," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    • Handle: RePEc:eee:apmaco:v:386:y:2020:i:c:s0096300320304744
    DOI: 10.1016/j.amc.2020.125516
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320304744
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125516?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. Yan, Yun & Dai, Weizhong & Wu, Longyuan & Zhai, Shuying, 2019. "Accurate gradient preserved method for solving heat conduction equations in double layers," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 58-85.
    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. Chinonso I. Nwankwo & Weizhong Dai & Ruihua Liu, 2023. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Computational Economics, Springer;Society for Computational Economics, vol. 62(3), pages 817-854, October.
    2. Chinonso Nwankwo & Weizhong Dai, 2020. "Multigrid Iterative Algorithm based on Compact Finite Difference Schemes and Hermite interpolation for Solving Regime Switching American Options," Papers 2008.00925, arXiv.org, revised Nov 2021.
    3. Chinonso Nwankwo & Weizhong Dai & Ruihua Liu, 2019. "Compact Finite Difference Scheme with Hermite Interpolation for Pricing American Put Options Based on Regime Switching Model," Papers 1908.04900, arXiv.org, revised Jun 2020.
    4. Chinonso Nwankwo & Weizhong Dai & Tony Ware, 2023. "Enhancing accuracy for solving American CEV model with high-order compact scheme and adaptive time stepping," Papers 2309.03984, arXiv.org, revised Sep 2023.

    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:apmaco:v:386:y:2020:i:c:s0096300320304744. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.