IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp794-811.html
   My bibliography  Save this article

Difference methods for parabolic equations with Robin condition

Author

Listed:
  • Sapa, Lucjan

Abstract

Classical solutions of nonlinear second-order partial differential functional equations of parabolic type with the Robin condition are approximated in the paper by solutions of associated boundedness-preserving implicit difference functional equations. It is proved that the discrete solutions uniquely exist, they are uniformly bounded with respect to meshes and the numerical method is convergent and stable. We also find the error estimate and its asymptotic behavior. The properties of some auxiliary nonlinear discrete recurrent equations are showed. The proofs are based on the comparison technique and the Banach fixed-point theorem.

Suggested Citation

  • Sapa, Lucjan, 2018. "Difference methods for parabolic equations with Robin condition," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 794-811.
  • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:794-811
    DOI: 10.1016/j.amc.2017.10.061
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317307701
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.amc.2017.10.061?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. Qin, Wendi & Ding, Deqiong & Ding, Xiaohua, 2015. "Two boundedness and monotonicity preserving methods for a generalized Fisher-KPP equation," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 552-567.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Hazrat Ali & Md. Kamrujjaman & Md. Shafiqul Islam, 2022. "An Advanced Galerkin Approach to Solve the Nonlinear \\[6pt]Reaction-Diffusion Equations With Different Boundary Conditions," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 14(1), pages 1-30, March.

    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. Macías-Díaz, J.E., 2018. "A numerically efficient Hamiltonian method for fractional wave equations," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 231-248.
    2. Macías-Díaz, J.E. & Hendy, A.S. & De Staelen, R.H., 2018. "A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 1-14.
    3. Deng, Dingwen & Xiong, Xiaohong, 2024. "Explicit, non-negativity-preserving and maximum-principle-satisfying finite difference scheme for the nonlinear Fisher's equation," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    4. Yan, Jingye & Zhang, Hong & Liu, Ziyuan & Song, Songhe, 2020. "Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation," Applied Mathematics and Computation, Elsevier, vol. 367(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:321:y:2018:i:c:p:794-811. 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.