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Applying the modified block-pulse functions to solve the three-dimensional Volterra–Fredholm integral equations

Author

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  • Mirzaee, Farshid
  • Hadadiyan, Elham

Abstract

The main aim of this work is to give further studies for the multi-dimensional integral equations. In this work, we solve special types of the three-dimensional Volterra–Fredholm linear integral equations of the second kind via the modified block-pulse functions. Some theorems are included to show convergence and advantage of the method. We solve some examples to investigate the applicability and simplicity of the method. The numerical results confirm that the method is efficient and simple.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:759-767
    DOI: 10.1016/j.amc.2015.05.125
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    Citations

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    Cited by:

    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 & 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.
    3. 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.
    4. 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.
    5. Pan, Yubin & Huang, Jin & Ma, Yanying, 2019. "Bernstein series solutions of multidimensional linear and nonlinear Volterra integral equations with fractional order weakly singular kernels," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 149-161.

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