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Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method

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Abstract

A numerical method to solve the nonlinear Volterra integral equations of the first kind with discontinuous kernels is proposed. Usage of operational matrices for this kind of equation is a cost-efficient scheme. Shifted Legendre polynomials are applied for solving Volterra integral equations with discontinuous kernels by converting the equation to a system of nonlinear algebraic equations. The convergence analysis is given for the approximated solution and numerical examples are demonstrated to denote the precision of the proposed method.

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Authors and Affiliations

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

    Simin Aghaei Amirkhizi & Yaghoub Mahmoudi

  2. Department of Mathematics, Shabestar Branch, Islamic Azad University, Shabestar, Iran

    Ali Salimi Shamloo

Authors
  1. Simin Aghaei Amirkhizi
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  2. Yaghoub Mahmoudi
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  3. Ali Salimi Shamloo
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Correspondence to Yaghoub Mahmoudi.

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Amirkhizi, S.A., Mahmoudi, Y. & Shamloo, A.S. Solving Nonlinear Volterra Integral Equations of the First Kind with Discontinuous Kernels by Using the Operational Matrix Method. Comput. Math. and Math. Phys. 63, 2069–2080 (2023). https://doi.org/10.1134/S0965542523110015

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