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Approximate solution of nonlinear Fredholm integral equations of the second kind using a class of Hermite interpolation polynomials

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  • Karamollahi, Nasibeh
  • Heydari, Mohammad
  • Loghmani, Ghasem Barid

Abstract

A particular case of the Hermite interpolation method, namely the two-point Taylor formula, is utilized to construct a numerical technique for solving Fredholm integral equations (FIEs) of the second kind. This method can be applied to approximate the solution of both linear and nonlinear FIEs, and systems of nonlinear FIEs. The sufficient conditions to guarantee the convergence of the proposed method are provided through our analytical studies. Also, the error estimation is presented for this method. Furthermore, the efficiency of the method is confirmed by applying it to solve several illustrative examples. Numerical experiments confirm that the method is easy to implement and gives accurate approximations in acceptable computational times.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:187:y:2021:i:c:p:414-432
    DOI: 10.1016/j.matcom.2021.03.015
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    References listed on IDEAS

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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. 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.
    3. Esmaeilbeigi, Mohsen & Mirzaee, Farshid & Moazami, Davoud, 2017. "A meshfree method for solving multidimensional linear Fredholm integral equations on the hypercube domains," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 236-246.
    4. Mirzaee, Farshid & Hadadiyan, Elham, 2015. "Numerical solution of linear Fredholm integral equations via two-dimensional modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 805-816.
    5. Mirzaee, Farshid & Samadyar, Nasrin, 2019. "Numerical solution based on two-dimensional orthonormal Bernstein polynomials for solving some classes of two-dimensional nonlinear integral equations of fractional order," Applied Mathematics and Computation, Elsevier, vol. 344, pages 191-203.
    6. 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.
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