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Application of Fibonacci collocation method for solving Volterra–Fredholm integral equations

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  • Mirzaee, Farshid
  • Hoseini, Seyede Fatemeh

Abstract

In this paper, a new matrix method based on Fibonacci polynomials and collocation points is proposed for numerically solving the Volterra–Fredholm integral equations. In fact, the approximate solution of the problem in the truncated Fibonacci series form is obtained by this method. Also, convergence analysis of the proposed method is provided under several mild conditions. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:273:y:2016:i:c:p:637-644
    DOI: 10.1016/j.amc.2015.10.035
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    References listed on IDEAS

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    1. Yousefi, S. & Razzaghi, M., 2005. "Legendre wavelets method for the nonlinear Volterra–Fredholm integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 70(1), pages 1-8.
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    1. Amiri, Sadegh & Hajipour, Mojtaba & Baleanu, Dumitru, 2020. "A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    2. Bulai, I.M. & De Bonis, M.C. & Laurita, C. & Sagaria, V., 2023. "Modeling metastatic tumor evolution, numerical resolution and growth prediction," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 721-740.
    3. Mirzaee, Farshid & Hoseini, Seyede Fatemeh, 2017. "A new collocation approach for solving systems of high-order linear Volterra integro-differential equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 272-282.
    4. 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).

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