IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i12p2248-d465252.html
   My bibliography  Save this article

Complex Ginzburg–Landau Equation with Generalized Finite Differences

Author

Listed:
  • Eduardo Salete

    (ETSII, UNED, 28080 Madrid, Spain
    These authors contributed equally to this work.)

  • Antonio M. Vargas

    (Departamento de Análisis Matemático y Matemática Aplicada, UCM, 28080 Madrid, Spain
    These authors contributed equally to this work.)

  • Ángel García

    (ETSII, UNED, 28080 Madrid, Spain
    These authors contributed equally to this work.)

  • Mihaela Negreanu

    (Departamento de Análisis Matemático y Matemática Aplicada, Instituto de Matemática Interdisciplinar, UCM, 28080 Madrid, Spain
    These authors contributed equally to this work.)

  • Juan J. Benito

    (ETSII, UNED, 28080 Madrid, Spain
    These authors contributed equally to this work.)

  • Francisco Ureña

    (ETSII, UNED, 28080 Madrid, Spain
    These authors contributed equally to this work.)

Abstract

In this paper we obtain a novel implementation for irregular clouds of nodes of the meshless method called Generalized Finite Difference Method for solving the complex Ginzburg–Landau equation. We derive the explicit formulae for the spatial derivative and an explicit scheme by splitting the equation into a system of two parabolic PDEs. We prove the conditional convergence of the numerical scheme towards the continuous solution under certain assumptions. We obtain a second order approximation as it is clear from the numerical results. Finally, we provide several examples of its application over irregular domains in order to test the accuracy of the explicit scheme, as well as comparison with other numerical methods.

Suggested Citation

  • Eduardo Salete & Antonio M. Vargas & Ángel García & Mihaela Negreanu & Juan J. Benito & Francisco Ureña, 2020. "Complex Ginzburg–Landau Equation with Generalized Finite Differences," Mathematics, MDPI, vol. 8(12), pages 1-13, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:12:p:2248-:d:465252
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/12/2248/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/12/2248/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Benito JJ & Garcıa A & Urena F & Gavete ML & Gavete L & Negreanu M & Vargas AM, 2019. "Numerical Simulation of a Mathematical Model for Cancer Cell Invasion," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 23(2), pages 17355-17359, November.
    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. Qiang Wang & Pyeoungkee Kim & Wenzhen Qu, 2022. "A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions," Mathematics, MDPI, vol. 10(3), pages 1-14, February.
    2. Vyacheslav Trofimov & Maria Loginova & Mikhail Fedotov & Daniil Tikhvinskii & Yongqiang Yang & Boyuan Zheng, 2022. "Conservative Finite-Difference Scheme for 1D Ginzburg–Landau Equation," Mathematics, MDPI, vol. 10(11), pages 1-24, June.
    3. Francisco Ureña & Ángel García & Antonio M. Vargas, 2022. "Preface to “Applications of Partial Differential Equations in Engineering”," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

    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.

      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:8:y:2020:i:12:p:2248-:d:465252. 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: 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.