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A meshfree method for solving multidimensional linear Fredholm integral equations on the hypercube domains

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  • Esmaeilbeigi, Mohsen
  • Mirzaee, Farshid
  • Moazami, Davoud

Abstract

The main purpose of this article is to describe a numerical scheme for solving multidimensional linear Fredholm integral equations of the second kind on the hypercube domains. The method is based on interpolation by radial basis functions (RBFs) to approximate the solution of the linear Fredholm integral equations. Error analysis is presented for this method. Finally, several examples are given and numerical examples are presented to demonstrate the validity and applicability of the method.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:298:y:2017:i:c:p:236-246
    DOI: 10.1016/j.amc.2016.11.020
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    References listed on IDEAS

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    1. 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.
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    Cited by:

    1. Akbari, Tahereh & Esmaeilbeigi, Mohsen & Moazami, Davoud, 2024. "A stable meshless numerical scheme using hybrid kernels to solve linear Fredholm integral equations of the second kind and its applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 220(C), pages 1-28.
    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. Maleknejad, Khosrow & Rashidinia, Jalil & Eftekhari, Tahereh, 2018. "Numerical solution of three-dimensional Volterra–Fredholm integral equations of the first and second kinds based on Bernstein’s approximation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 272-285.

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    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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