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Solvability of Quadratic Integral Equations with Singular Kernel

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Abstract

In this paper, we discuss the existence and uniqueness of solution of the singular quadratic integral equation (SQIE). The Fredholm integral term is assumed in position with singular kernel. Under certain conditions and new discussions, the singular kernel  will tend to a  logarithmic kernel. Then,  using Chebyshev  polynomial, a main of spectral relationships are stated and used to obtain the solution of the singular quadratic integral equation with the logarithmic kernel and a smooth kernel. Finally, the Fredholm integral equation of the second kind is established and its solution is discussed, also numerical results are obtained and the error, in each case, is computed.

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ACKNOWLEDGMENTS

The authors are very grateful to the referees and editors for their useful comments that led to improvement of our manuscript.

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Authors and Affiliations

  1. Benha University, Benha, Egypt

    M. A. Abdel-Aty, M. A. Abdou & A. A. Soliman

  2. Alexandria University, Alexandria, Egypt

    M. A. Abdel-Aty, M. A. Abdou & A. A. Soliman

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  1. M. A. Abdel-Aty
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  2. M. A. Abdou
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  3. A. A. Soliman
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Correspondence to M. A. Abdel-Aty, M. A. Abdou or A. A. Soliman.

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Abdel-Aty, M.A., Abdou, M.A. & Soliman, A.A. Solvability of Quadratic Integral Equations with Singular Kernel. J. Contemp. Mathemat. Anal. 57, 12–25 (2022). https://doi.org/10.3103/S1068362322010022

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