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Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation

Author

Listed:
  • Ioannis Dassios
  • Fairouz Tchier
  • F. M. O. Tawfiq

Abstract

This paper deals with the numerical solution of the Abel integral equation based on Müntz–Legendre wavelets. To this end, the Abel integral operator is represented by Müntz–Legendre wavelets as an operational matrix. To find this matrix, we use the similarity between the Abel integral operator and the fractional integral operator. The proposed method can be easily used to solve weakly singular Volterra integral equations. We have proved the convergence of the proposed method. To demonstrate the ability and accuracy of the method, some numerical examples are presented.

Suggested Citation

  • Ioannis Dassios & Fairouz Tchier & F. M. O. Tawfiq, 2022. "Pseudospectral Method Based on Müntz–Legendre Wavelets for Solving the Abel Integral Equation," Journal of Mathematics, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jjmath:v:2022:y:2022:i:1:n:2251623
    DOI: 10.1155/2022/2251623
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    References listed on IDEAS

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    1. Abdul-Majid Wazwaz, 2011. "Linear and Nonlinear Integral Equations," Springer Books, Springer, number 978-3-642-21449-3, January.
    2. Haifa Bin Jebreen & Fairouz Tchier & à tila Madureira Bueno, 2021. "A New Scheme for Solving Multiorder Fractional Differential Equations Based on Müntz–Legendre Wavelets," Complexity, Hindawi, vol. 2021, pages 1-9, July.
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