IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v342y2019icp118-129.html
   My bibliography  Save this article

Unconditionally stable compact theta schemes for solving the linear and semi-linear fourth-order diffusion equations

Author

Listed:
  • Ran, Maohua
  • Luo, Taibai
  • Zhang, Li

Abstract

This paper is concerned with numerical methods for solving a class of fourth-order diffusion equations. Combining the compact difference operator in space discretization and the linear θ method in time, the compact theta scheme for the linear problem is first proposed. By virtue of the Fourier method, the suggested scheme is shown to be unconditionally stable and convergent in the discrete L2-norm for any θ ∈ [1/2, 1]. And then this idea is generalized to the semi-linear case, the corresponding compact theta scheme is constructed and analyzed in detail. Numerical experiments corresponding to the linear and semi-linear situations are carried out to support our theoretical statements.

Suggested Citation

  • Ran, Maohua & Luo, Taibai & Zhang, Li, 2019. "Unconditionally stable compact theta schemes for solving the linear and semi-linear fourth-order diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 118-129.
    • Handle: RePEc:eee:apmaco:v:342:y:2019:i:c:p:118-129
    DOI: 10.1016/j.amc.2018.09.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318307987
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.09.026?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. Mohanty, R.K. & McKee, Sean & Kaur, Deepti, 2017. "A class of two-level implicit unconditionally stable methods for a fourth order parabolic equation," Applied Mathematics and Computation, Elsevier, vol. 309(C), pages 272-280.
    2. Mohanty, R.K. & Kaur, Deepti, 2016. "High accuracy implicit variable mesh methods for numerical study of special types of fourth order non-linear parabolic equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 678-696.
    3. Zhang, Qifeng & Chen, Mengzhe & Xu, Yinghong & Xu, Dinghua, 2018. "Compact θ-method for the generalized delay diffusion equation," Applied Mathematics and Computation, Elsevier, vol. 316(C), pages 357-369.
    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. Qin, Hongyu & Zhang, Qifeng & Wan, Shaohua, 2019. "The continuous Galerkin finite element methods for linear neutral delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 76-85.
    2. Mohanty, R.K. & Kaur, Deepti & Singh, Swarn, 2019. "A class of two- and three-level implicit methods of order two in time and four in space based on half-step discretization for two-dimensional fourth order quasi-linear parabolic equations," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 68-87.
    3. Zhang, Qifeng & Ren, Yunzhu & Lin, Xiaoman & Xu, Yinghong, 2019. "Uniform convergence of compact and BDF methods for the space fractional semilinear delay reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 91-110.
    4. Kaur, Deepti & Mohanty, R.K., 2020. "Highly accurate compact difference scheme for fourth order parabolic equation with Dirichlet and Neumann boundary conditions: Application to good Boussinesq equation," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    5. Qin, Hongyu & Wu, Fengyan & Ding, Deng, 2022. "A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    6. Jian, Huan-Yan & Huang, Ting-Zhu & Ostermann, Alexander & Gu, Xian-Ming & Zhao, Yong-Liang, 2021. "Fast numerical schemes for nonlinear space-fractional multidelay reaction-diffusion equations by implicit integration factor methods," Applied Mathematics and Computation, Elsevier, vol. 408(C).

    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:342:y:2019:i:c:p:118-129. 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.