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On the regularization method for Fredholm integral equations with odd weakly singular kernel

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Abstract

In this paper, we propose a numerical method to approach the solution of a Fredholm integral equation with a weakly singular kernel by applying the convolution product as a regularization operator and the Fourier series as a projection. Preliminary numerical results show that the order of convergence of the method is better than the one of conventional projection methods.

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References

  • Adams RA (1975) Sobolev spaces. Academic Press, New York, pp 22–38

    Google Scholar 

  • Ahues M, d’Almeida FD, Fernandes RR (2009) Piecewise constant Galerkin approximations of wealkly singular integral equations. Int J Pure Appl Math 4:569–580

    MATH  Google Scholar 

  • Amosov AA, Youssef YE (2016) Error estimates of projection type methods for solving weakly singular integral equations. J Math Sci 216:182–218

    Article  MathSciNet  MATH  Google Scholar 

  • Atkinson K, Han W (2001) Theoretical numerical analysis: a functional analysis framework. Springer, New York, pp 342–404

    MATH  Google Scholar 

  • Davidson KR, Donsig AP (2009) Real analysis and applications. Springer, New York

    MATH  Google Scholar 

  • Debbar R, Guebbai H, Zereg Z (2016) Improving the convergence order of the regularization method for Fredholm integral equations of the second kind. Appl Math Comput 289:204–213

    MathSciNet  Google Scholar 

  • Guebbai H, Grammont L (2014) A new degenerate kernel method for a weakly singular integral equation. Appl Math Comput 230:414–427

    MathSciNet  MATH  Google Scholar 

  • http://www.wolframalpha.com/calculators/integral-calculator/. Accessed 19 Apr 2018

  • Lemita S, Guebbai H (2017) New process to approach linear Fredholm integral equations defined on large interval. Asian Eur J Math. https://doi.org/10.1142/S1793557119500098

  • Tikhomirov VM (1976) Some problems of approximation theory. Moscow University, Moscow

    Google Scholar 

  • Zygmund A (1959) Trigonometric series. The Cambridge University Press, Cambridge

    MATH  Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques, Université Mohamed-Chérif Messaadia Souk Ahras, B.P. 1553, 41000, Souk Ahras, Algeria

    Noureddine Benrabia

  2. Département de Mathématiques, Université 8 Mai 1945 Guelma, B.P. 401, 24000, Guelma, Algeria

    Hamza Guebbai

Authors
  1. Noureddine Benrabia
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  2. Hamza Guebbai
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Corresponding author

Correspondence to Hamza Guebbai.

Additional information

Communicated by Delfim F. M. Torres.

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Benrabia, N., Guebbai, H. On the regularization method for Fredholm integral equations with odd weakly singular kernel. Comp. Appl. Math. 37, 5162–5174 (2018). https://doi.org/10.1007/s40314-018-0625-3

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  • DOI: https://doi.org/10.1007/s40314-018-0625-3

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