IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v315y2017icp424-444.html
   My bibliography  Save this article

A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions

Author

Listed:
  • Assari, Pouria
  • Dehghan, Mehdi

Abstract

The main intention of the current paper is to describe a scheme for the numerical solution of boundary integral equations of the second kind with logarithmic singular kernels. These types of integral equations result from boundary value problems of Laplace’s equations with linear Robin boundary conditions. The method approximates the solution using the radial basis function (RBF) expansion with polynomial precision in the discrete collocation method. The collocation method for solving logarithmic boundary integral equations encounters more difficulties for computing the singular integrals which cannot be approximated by the classical quadrature formulae. To overcome this problem, we utilize the non-uniform composite Gauss–Legendre integration rule and employ it to estimate the singular logarithm integrals appeared in the method. Since the scheme is based on the use of scattered points spread on the analyzed domain and does not need any domain elements, we can call it as the meshless discrete collocation method. The new algorithm is successful and easy to solve various types of boundary integral equations with singular kernels. We also provide the error estimate of the proposed method. The efficiency and accuracy of the new approach are illustrated by some numerical examples.

Suggested Citation

  • Assari, Pouria & Dehghan, Mehdi, 2017. "A meshless discrete collocation method for the numerical solution of singular-logarithmic boundary integral equations utilizing radial basis functions," Applied Mathematics and Computation, Elsevier, vol. 315(C), pages 424-444.
    • Handle: RePEc:eee:apmaco:v:315:y:2017:i:c:p:424-444
    DOI: 10.1016/j.amc.2017.07.073
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317305349
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.07.073?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.

    Citations

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


    Cited by:

    1. Akbari, Tahereh & Esmaeilbeigi, Mohsen & Moazami, Davoud, 2024. "A stable meshless numerical scheme using hybrid kernels to solve linear Fredholm integral equations of the second kind and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 1-28.
    2. Assari, Pouria & Dehghan, Mehdi, 2019. "A meshless local discrete Galerkin (MLDG) scheme for numerically solving two-dimensional nonlinear Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 249-265.
    3. Kumhar, Raju & Kundu, Santimoy & Pandit, Deepak Kr. & Gupta, Shishir, 2020. "Green’s function and surface waves in a viscoelastic orthotropic FGM enforced by an impulsive point source," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    4. Xu, Fei & Huang, Qiumei, 2019. "An accurate a posteriori error estimator for semilinear Neumann problem and its applications," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    5. Pan, Yubin & Huang, Jin & Ma, Yanying, 2019. "Bernstein series solutions of multidimensional linear and nonlinear Volterra integral equations with fractional order weakly singular kernels," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 149-161.

    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:315:y:2017:i:c:p:424-444. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.