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An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition

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Abstract

In this paper, a linear singularly perturbed Fredholm integro-differential initial value problem with integral condition is being considered. On a Shishkin-type mesh, a fitted finite difference approach is applied using a composite trapezoidal rule in both; in the integral part of equation and in the initial condition. The proposed technique acquires a uniform second-order convergence in respect to perturbation parameter. Further provided the numerical results to support the theoretical estimates.

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Author notes

  1. Ilhame Amirali and Gabil M. Amiraliyev have contributed equally to this work.

Authors and Affiliations

  1. Department of Information Technology, Kırklareli University, Kırklareli, 39100, Turkey

    Muhammet Enes Durmaz

  2. Department of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce, 81620, Turkey

    Ilhame Amirali

  3. Department of Mathematics, Faculty of Arts and Sciences, Erzincan Binali Yıldırım University, Erzincan, 24100, Turkey

    Gabil M. Amiraliyev

Authors
  1. Muhammet Enes Durmaz
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  2. Ilhame Amirali
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  3. Gabil M. Amiraliyev
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Correspondence to Muhammet Enes Durmaz.

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Durmaz, M.E., Amirali, I. & Amiraliyev, G.M. An efficient numerical method for a singularly perturbed Fredholm integro-differential equation with integral boundary condition. J. Appl. Math. Comput. 69, 505–528 (2023). https://doi.org/10.1007/s12190-022-01757-4

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