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A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations

Author

Listed:
  • Musa Cakir

    (Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

  • Baransel Gunes

    (Department of Mathematics, Faculty of Science, Van Yuzuncu Yil University, Van 65080, Turkey
    These authors contributed equally to this work.)

Abstract

This paper presents a ε -uniform and reliable numerical scheme to solve second-order singularly perturbed Volterra–Fredholm integro-differential equations. Some properties of the analytical solution are given, and the finite difference scheme is established on a non-uniform mesh by using interpolating quadrature rules and the linear basis functions. An error analysis is successfully carried out on the Boglaev–Bakhvalov-type mesh. Some numerical experiments are included to authenticate the theoretical findings. In this regard, the main advantage of the suggested method is to yield stable results on layer-adapted meshes.

Suggested Citation

  • Musa Cakir & Baransel Gunes, 2022. "A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3560-:d:929390
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    References listed on IDEAS

    as
    1. K. Issa & F. Salehi, 2017. "Approximate Solution of Perturbed Volterra-Fredholm Integrodifferential Equations by Chebyshev-Galerkin Method," Journal of Mathematics, Hindawi, vol. 2017, pages 1-6, January.
    2. Alvandi, Azizallah & Paripour, Mahmoud, 2019. "The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 151-160.
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