IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v185y2021icp153-173.html
   My bibliography  Save this article

On solving elliptic boundary value problems using a meshless method with radial polynomials

Author

Listed:
  • Ku, Cheng-Yu
  • Xiao, Jing-En
  • Liu, Chih-Yu
  • Lin, Der-Guey

Abstract

This paper presents the meshless method using radial polynomials with the combination of the multiple source collocation scheme for solving elliptic boundary value problems. In the proposed method, the basis function is based on the radial polynomials, which is different from the conventional radial basis functions that approximate the solution using the specific function such as the multiquadric function with the shape parameter for infinitely differentiable. The radial polynomial basis function is a non-singular series function in nature which is infinitely smooth and differentiable in nature without using the shape parameter. With the combination of the multiple source collocation scheme, the center point is regarded as the source point for the interpolation of the radial polynomials. Numerical solutions in multiple dimensions are approximated by applying the radial polynomials with given terms of the radial polynomials. The comparison of the proposed method with the radial basis function collocation method (RBFCM) using the multiquadric and polyharmonic spline functions is conducted. Results demonstrate that the accuracy obtained from the proposed method is better than that of the conventional RBFCM with the same number of collocation points. In addition, highly accurate solutions with the increase of radial polynomial terms may be obtained.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:185:y:2021:i:c:p:153-173
    DOI: 10.1016/j.matcom.2020.12.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475420304675
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2020.12.012?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. Biazar, Jafar & Hosami, Mohammad, 2017. "An interval for the shape parameter in radial basis function approximation," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 131-149.
    2. Lin, Ji & Zhao, Yuxiang & Watson, Daniel & Chen, C.S., 2020. "The radial basis function differential quadrature method with ghost points," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 173(C), pages 105-114.
    3. Lei Mu & Zhi-hong He & Shi-kui Dong, 2015. "Reproducing Kernel Particle Method for Radiative Heat Transfer in 1D Participating Media," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-11, March.
    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. 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.

    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. Cheng-Yu Ku & Jing-En Xiao & Chih-Yu Liu, 2020. "A Novel Meshfree Approach with a Radial Polynomial for Solving Nonhomogeneous Partial Differential Equations," Mathematics, MDPI, vol. 8(2), pages 1-22, February.
    2. Chih-Yu Liu & Cheng-Yu Ku & Li-Dan Hong & Shih-Meng Hsu, 2021. "Infinitely Smooth Polyharmonic RBF Collocation Method for Numerical Solution of Elliptic PDEs," Mathematics, MDPI, vol. 9(13), pages 1-22, June.
    3. Zhu, Xiaomin & Dou, Fangfang & Karageorghis, Andreas & Chen, C.S., 2020. "A fictitious points one–step MPS–MFS technique," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    4. Su, LingDe, 2019. "A radial basis function (RBF)-finite difference (FD) method for the backward heat conduction problem," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 232-247.
    5. R. Cavoretto & A. Rossi & M. S. Mukhametzhanov & Ya. D. Sergeyev, 2021. "On the search of the shape parameter in radial basis functions using univariate global optimization methods," Journal of Global Optimization, Springer, vol. 79(2), pages 305-327, February.

    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:matcom:v:185:y:2021:i:c:p:153-173. 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: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    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.