IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v354y2019icp58-85.html
   My bibliography  Save this article

Accurate gradient preserved method for solving heat conduction equations in double layers

Author

Listed:
  • Yan, Yun
  • Dai, Weizhong
  • Wu, Longyuan
  • Zhai, Shuying

Abstract

Analyzing heat transfer in layered structures is important for the design and operation of devices and the optimization of thermal processing of materials. Existing numerical methods dealing with layered structures if using only three grid points across the interface usually provide only a second-order truncation error. Obtaining a numerical scheme using three grid points across the interface so that the overall numerical scheme is unconditionally stable and convergent with higher-order accuracy is mathematically challenging. In this study, we develop a higher-order accurate finite difference method using three grid points across the interface by preserving the first-order derivative, ux, in the interfacial condition and/or the boundary condition. As such, when the compact fourth-order accurate Padé scheme is used at the interior points, the overall scheme maintains to be higher-order accurate. Stability and convergence of the scheme are analyzed. Finally, four examples are given to test the obtained numerical method. Results show that the convergence order in space is close to 4.0, which coincides with the theoretical analysis.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:354:y:2019:i:c:p:58-85
    DOI: 10.1016/j.amc.2019.02.038
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300319301420
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2019.02.038?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.

    Citations

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


    Cited by:

    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 & 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.
    3. 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.
    4. 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).
    5. 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:354:y:2019:i:c:p:58-85. 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: 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.