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An improved numerical iterative method for solving nonlinear fuzzy Fredholm integral equations via Picard’s method and generalized quadrature rule

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Abstract

In this paper, we approximate the integral of fuzzy-number-valued functions using generalized quadrature rule and obtain its error estimate. Utilizing the generalized quadrature rule and successive approximations method, we construct an iterative approach to find the numerical approximation of solutions. Moreover, we investigate the error analysis of the numerical method, which guarantees pointwise convergence. Then we apply the presented method to two numerical experiments to present the accuracy and convergence of the method.

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Authors and Affiliations

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

    Shokrollah Ziari

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

    Tofigh Allahviranloo

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

    Witold Pedrycz

Authors
  1. Shokrollah Ziari
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  2. Tofigh Allahviranloo
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  3. Witold Pedrycz
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Correspondence to Shokrollah Ziari.

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Communicated by Hui Liang.

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Ziari, S., Allahviranloo, T. & Pedrycz, W. An improved numerical iterative method for solving nonlinear fuzzy Fredholm integral equations via Picard’s method and generalized quadrature rule. Comp. Appl. Math. 40, 230 (2021). https://doi.org/10.1007/s40314-021-01616-1

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  • DOI: https://doi.org/10.1007/s40314-021-01616-1

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