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Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations

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  • Zare, Farideh
  • Heydari, Mohammad
  • Loghmani, Ghasem Barid

Abstract

In the current study, an efficient iterative scheme which is based on the two powerful tools called the quasilinearization method and the Jacobi-Galerkin method is proposed to solve a type of functional Volterra integral equations. According to the iterative structure of the proposed method, an error analysis of the method is provided. This method can overcome the difficulty of solving nonlinear system of algebraic equations associated with the Galerkin method in treating nonlinear functional Volterra integral equations directly. Moreover, under sufficient conditions, the suggested method has spectral accuracy. In the end, several numerical experiments are reported to confirm the efficiency and accuracy of the proposed scheme.

Suggested Citation

  • Zare, Farideh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2024. "Convergence analysis of an iterative scheme to solve a family of functional Volterra integral equations," Applied Mathematics and Computation, Elsevier, vol. 477(C).
    • Handle: RePEc:eee:apmaco:v:477:y:2024:i:c:s0096300324002601
    DOI: 10.1016/j.amc.2024.128799
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    References listed on IDEAS

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    1. Mirzaee, Farshid & Solhi, Erfan & Naserifar, Shiva, 2021. "Approximate solution of stochastic Volterra integro-differential equations by using moving least squares scheme and spectral collocation method," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    2. Karamollahi, Nasibeh & Heydari, Mohammad & Loghmani, Ghasem Barid, 2021. "Approximate solution of nonlinear Fredholm integral equations of the second kind using a class of Hermite interpolation polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 414-432.
    3. Singh, Randhir & Guleria, Vandana & Singh, Mehakpreet, 2020. "Haar wavelet quasilinearization method for numerical solution of Emden–Fowler type equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 174(C), pages 123-133.
    4. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2016. "Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 637-644.
    5. Torkaman, Soraya & Heydari, Mohammad & Loghmani, Ghasem Barid, 2023. "A combination of the quasilinearization method and linear barycentric rational interpolation to solve nonlinear multi-dimensional Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 366-397.
    6. Sudhakar G. Pandit, 1997. "Quadratically converging iterative schemes for nonlinear Volterra integral equations and an application," International Journal of Stochastic Analysis, Hindawi, vol. 10, pages 1-10, January.
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