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A spectral collocation method with piecewise trigonometric basis functions for nonlinear Volterra–Fredholm integral equations

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  • Amiri, Sadegh
  • Hajipour, Mojtaba
  • Baleanu, Dumitru

Abstract

The aim of this paper is to investigate an efficient numerical method based on a novel shifted piecewise cosine basis for solving Volterra–Fredholm integral equations of the second kind. Using operational matrices of integration for the proposed basis functions, this integral equation is transformed into a system of nonlinear algebraic equations. The convergence and error analysis of the proposed method are studied. Some comparative results are provided to verify the efficiency of the presented method.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:370:y:2020:i:c:s0096300319309075
    DOI: 10.1016/j.amc.2019.124915
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    References listed on IDEAS

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    1. Mirzaee, Farshid & Hadadiyan, Elham, 2016. "Numerical solution of Volterra–Fredholm integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 110-123.
    2. Grammont, Laurence & Vasconcelos, Paulo B. & Ahues, Mario, 2016. "A modified iterated projection method adapted to a nonlinear integral equation," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 432-441.
    3. 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.
    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. Mirzaee, Farshid & Hadadiyan, Elham, 2015. "Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 759-767.
    6. Micula, Sanda, 2015. "An iterative numerical method for Fredholm–Volterra integral equations of the second kind," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 935-942.
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    Cited by:

    1. 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.

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