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Successive Approximations Method for Fuzzy Fredholm-Volterra Integral equations of the Second Kind

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Advances in Fuzzy Integral and Differential Equations

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 412))

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Abstract

In this paper, the successive approximations technique based on the trapezoidal quadrature rule is used for solving the fuzzy Fredholm-Volterra integral equations in two dimensions. We first present the way to approximate the value of the integral of any fuzzy-valued function based on the quadrature rule, that can be sequentially applied to evaluate the multiple integral. The convergence of the method will be investigated by giving error bounds for the approximate solution. Finally, a numerical experiment is included to demonstrate that the numerical results are consistent with the theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Firoozkooh Branch, Islamic Azad University, Firoozkooh, Iran

    S. Ziari

  2. Department of Mathematics and Informatics, University of Oradea, Universitatii 1, 410087, Oradea, Romania

    A. M. Bica

  3. Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

    R. Ezzati

Authors
  1. S. Ziari
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  2. A. M. Bica
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  3. R. Ezzati
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Correspondence to S. Ziari .

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Editors and Affiliations

  1. Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul, Turkey

    Tofigh Allahviranloo

  2. Faculty of Engineering and Natural Sciences, Bahçeşehir University, Istanbul, Turkey

    Soheil Salahshour

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Ziari, S., Bica, A.M., Ezzati, R. (2022). Successive Approximations Method for Fuzzy Fredholm-Volterra Integral equations of the Second Kind. In: Allahviranloo, T., Salahshour, S. (eds) Advances in Fuzzy Integral and Differential Equations. Studies in Fuzziness and Soft Computing, vol 412. Springer, Cham. https://doi.org/10.1007/978-3-030-73711-5_9

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