IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i18p3935-d1241300.html
   My bibliography  Save this article

A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems

Author

Listed:
  • Chih-Yu Liu

    (Department of Civil Engineering, National Central University, Taoyuan 320317, Taiwan)

  • Cheng-Yu Ku

    (School of Engineering, National Taiwan Ocean University, Keelung 202301, Taiwan)

Abstract

Elliptic boundary value problems (BVPs) are widely used in various scientific and engineering disciplines that involve finding solutions to elliptic partial differential equations subject to certain boundary conditions. This article introduces a novel approach for solving elliptic BVPs using an artificial neural network (ANN)-based radial basis function (RBF) collocation method. In this study, the backpropagation neural network is employed, enabling learning from training data and enhancing accuracy. The training data consist of given boundary data from exact solutions and the radial distances between exterior fictitious sources and boundary points, which are used to construct RBFs, such as multiquadric and inverse multiquadric RBFs. The distinctive feature of this approach is that it avoids the discretization of the governing equation of elliptic BVPs. Consequently, the proposed ANN-based RBF collocation method offers simplicity in solving elliptic BVPs with only given boundary data and RBFs. To validate the model, it is applied to solve two- and three-dimensional elliptic BVPs. The results of the study highlight the effectiveness and efficiency of the proposed method, demonstrating its capability to deliver accurate solutions with minimal data input for solving elliptic BVPs while relying solely on given boundary data and RBFs.

Suggested Citation

  • Chih-Yu Liu & Cheng-Yu Ku, 2023. "A Novel ANN-Based Radial Basis Function Collocation Method for Solving Elliptic Boundary Value Problems," Mathematics, MDPI, vol. 11(18), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3935-:d:1241300
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/18/3935/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/18/3935/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ku, Cheng-Yu & Xiao, Jing-En & Liu, Chih-Yu & Lin, Der-Guey, 2021. "On solving elliptic boundary value problems using a meshless method with radial polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 153-173.
    2. Chih-Yu Liu & Cheng-Yu Ku, 2022. "A Simplified Radial Basis Function Method with Exterior Fictitious Sources for Elliptic Boundary Value Problems," Mathematics, MDPI, vol. 10(10), pages 1-23, May.
    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. Dmitry Stenkin & Vladimir Gorbachenko, 2024. "Mathematical Modeling on a Physics-Informed Radial Basis Function Network," Mathematics, MDPI, vol. 12(2), pages 1-11, January.

    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. Li-Dan Hong & Cheng-Yu Ku & Chih-Yu Liu, 2022. "A Novel Space-Time Marching Method for Solving Linear and Nonlinear Transient Problems," Mathematics, MDPI, vol. 10(24), pages 1-16, December.

    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:11:y:2023:i:18:p:3935-:d:1241300. 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.