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Meshless methods for one-dimensional oscillatory Fredholm integral equations

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  • Zaheer-ud-Din,
  • Siraj-ul-Islam,

Abstract

In this paper, efficient and simple algorithms based on Levin’s quadrature theory and our earlier work involving local radial basis function (RBF) and Chebyshev differentiation matrices, are adopted for numerical solution of one-dimensional highly oscillatory Fredholm integral equations. This work is focused on the comparative performance of local RBF meshless and pseudospectral procedures. We have tested the proposed methods on phase functions with and without stationary phase point(s), both on uniform and Chebyshev grid points. The proposed procedures are shown accurate and efficient, and therefore provide a reliable platform for the numerical solution of integral equations. From the numerical results, we draw some conclusions about accuracy, efficiency and robustness of the proposed approaches.

Suggested Citation

  • Zaheer-ud-Din, & Siraj-ul-Islam,, 2018. "Meshless methods for one-dimensional oscillatory Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 156-173.
    • Handle: RePEc:eee:apmaco:v:324:y:2018:i:c:p:156-173
    DOI: 10.1016/j.amc.2017.11.061
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    Cited by:

    1. Siraj-ul-Islam, & Haider, Nadeem & Aziz, Imran, 2018. "Meshless and multi-resolution collocation techniques for parabolic interface models," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 313-332.
    2. Zaheer-ud-Din & Muhammad Ahsan & Masood Ahmad & Wajid Khan & Emad E. Mahmoud & Abdel-Haleem Abdel-Aty, 2020. "Meshless Analysis of Nonlocal Boundary Value Problems in Anisotropic and Inhomogeneous Media," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    3. Imtiaz Ahmad & Muhammad Ahsan & Zaheer-ud Din & Ahmad Masood & Poom Kumam, 2019. "An Efficient Local Formulation for Time–Dependent PDEs," Mathematics, MDPI, vol. 7(3), pages 1-18, February.

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