Numerical solution of nonlinear fuzzy Volterra-Hammerstein delay integral equations by using Legendre wavelets

Articles in Press

Document Type : Original Article

Author

University of Kashan

Abstract

This paper presents a numerical method for solving fuzzy delay nonlinear Volterra-Hammerstein integral equations using Legendre wavelets. The importance of this class of equations is highlighted by their application to modeling epidemic problems, which represent a special case. After introducing preliminary definitions related to fuzzy equations and the basic characteristics of Legendre wavelets, we present the parametric form of nonlinear fuzzy delay Volterra-Hammerstein integral equations, which are essentially a system of nonlinear delay integral equations in a non-fuzzy state. We then employ Legendre wavelets, the collocation method, and the Gauss-Legendre quadrature rule to transform the integral equation into a system of algebraic equations that can be solved. Furthermore, we provide a detailed convergence analysis of the proposed method. The accuracy of the method is demonstrated through several numerical examples, with results compared to those obtained using Bernoulli and B-spline wavelet methods. These comparisons confirm the accuracy and efficiency of the presented method.

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Soft Computing Journal

Articles in Press, Accepted Manuscript
Available Online from 24 August 2025

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History

  • Receive Date: 22 September 2024
  • Revise Date: 15 November 2024
  • Accept Date: 12 December 2024

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