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Successive approximations method is used to solve nonlinear Volterra delay integral equations

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  • Behroozi, Hasan
  • Kazemi, Manochehr
  • Ezzati, Reza

Abstract

The current research introduces a new numerical iterative method that uses a quadrature formula and successive approximations to solve certain types of equations called nonlinear delay integral equations as Hammerstein Volterra type of the second kind. The convergence analysis and numerical stability of the method are also demonstrated. Additionally, by providing the numerical applications, we show to validate the theoretical results and showcase the method's accuracy. The investigation of this integral equation is significant as it encompasses a variant of a mathematical model used in epidemiology.

Suggested Citation

  • Behroozi, Hasan & Kazemi, Manochehr & Ezzati, Reza, 2025. "Successive approximations method is used to solve nonlinear Volterra delay integral equations," Applied Mathematics and Computation, Elsevier, vol. 507(C).
    • Handle: RePEc:eee:apmaco:v:507:y:2025:i:c:s0096300325002735
    DOI: 10.1016/j.amc.2025.129547
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    References listed on IDEAS

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    1. Kherraz, Tahar & Benbachir, Maamar & Lakrib, Mustapha & Samei, Mohammad Esmael & Kaabar, Mohammed K.A. & Bhanotar, Shailesh A., 2023. "Existence and uniqueness results for fractional boundary value problems with multiple orders of fractional derivatives and integrals," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    2. Kazemi, M. & Ezzati, R., 2016. "Existence of solution for some nonlinear two-dimensional Volterra integral equations via measures of noncompactness," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 165-171.
    3. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    4. Li Zhang & Jin Huang & Yubin Pan & Xiaoxia Wen, 2019. "A Mechanical Quadrature Method for Solving Delay Volterra Integral Equation with Weakly Singular Kernels," Complexity, Hindawi, vol. 2019, pages 1-12, June.
    5. Mosleh, Maryam & Otadi, Mahmood, 2015. "Least squares approximation method for the solution of Hammerstein–Volterra delay integral equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 105-110.
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