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On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions

Author

Listed:
  • Fairouz Tchier

    (Department of Mathematics, College of Science, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
    These authors contributed equally to this work.)

  • Ioannis Dassios

    (AMPSAS, University College Dublin, D04 Dublin, Ireland
    These authors contributed equally to this work.)

  • Ferdous Tawfiq

    (Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia
    These authors contributed equally to this work.)

  • Lakhdar Ragoub

    (Mathematics Department, University of Prince Mugrin, P.O. Box 41040, Madinah 42241, Saudi Arabia
    These authors contributed equally to this work.)

Abstract

In this paper, we apply the pseudospectral method based on the Chebyshev cardinal function to solve the parabolic partial integro-differential equations (PIDEs). Since these equations play a key role in mathematics, physics, and engineering, finding an appropriate solution is important. We use an efficient method to solve PIDEs, especially for the integral part. Unlike when using Chebyshev functions, when using Chebyshev cardinal functions it is no longer necessary to integrate to find expansion coefficients of a given function. This reduces the computation. The convergence analysis is investigated and some numerical examples guarantee our theoretical results. We compare the presented method with others. The results confirm the efficiency and accuracy of the method.

Suggested Citation

  • Fairouz Tchier & Ioannis Dassios & Ferdous Tawfiq & Lakhdar Ragoub, 2021. "On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions," Mathematics, MDPI, vol. 9(3), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:286-:d:490917
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    References listed on IDEAS

    as
    1. Imran Aziz & Imran Khan, 2017. "Numerical Solution of Partial Integrodifferential Equations of Diffusion Type," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-11, November.
    2. Heydari, M.H., 2020. "Chebyshev cardinal functions for a new class of nonlinear optimal control problems generated by Atangana–Baleanu–Caputo variable-order fractional derivative," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    3. Frédéric Abergel & Rémi Tachet, 2010. "A nonlinear partial integro-differential equation from mathematical finance," Post-Print hal-00611962, HAL.
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