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Numerical solution of Volterra–Fredholm integral equations via modification of hat functions

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  • Mirzaee, Farshid
  • Hadadiyan, Elham

Abstract

In this paper, a new numerical approach is developed for solving linear and nonlinear Volterra–Fredholm integral equations. The fundamental structure of the presented method is based on the modification of hat functions. The properties of modification of hat functions (MHFs) are first presented. After implementation of our scheme, the solution of the main problem would be transformed into the solution of a system of linear or nonlinear algebraic equations. Also, an error analysis is provided under several mild conditions. In addition, examples are presented to illustrate the pertinent features of the method and the results are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:280:y:2016:i:c:p:110-123
    DOI: 10.1016/j.amc.2016.01.038
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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. Nemati, S. & Lima, P.M., 2018. "Numerical solution of nonlinear fractional integro-differential equations with weakly singular kernels via a modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 327(C), pages 79-92.
    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. Mirzaee, Farshid & Hadadiyan, Elham, 2017. "Solving system of linear Stratonovich Volterra integral equations via modification of hat functions," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 254-264.

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