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Dergiler / Turkish Journal of Mathematics / 2022 / Cilt: 46 - Sayı: 1

Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition

Gabil M. AMIRALIYEV
Mustafa KUDU
Muhammet Enes DURMAZ
Sayfa
207–224
Yayın Tarihi
2022-11-01
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Some numerical examples have been solved and numerical outcomes are obtained.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions.
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Temel Bulgular & Veri:By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh.
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Sonuç & Katkı:Some numerical examples have been solved and numerical outcomes are obtained.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper, we deal with singularly perturbed Fredholm integro differential equation (SPFIDE) with mixed boundary conditions. By using interpolating quadrature rules and exponential basis function, fitted second order difference scheme has been constructed on a Shishkin mesh. The stability and convergence of the difference scheme have been analyzed in the discrete maximum norm. Some numerical examples have been solved and numerical outcomes are obtained.

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Bu Makaleye Atıf Yap

AMIRALIYEV, G. M., KUDU, M., DURMAZ, M. E. (2022). Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 1, 207–224. https://ajindex.com/articles/607299

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Kaynakça (4)

  1. Amiraliyev GM, Durmaz ME, Kudu M. Uniform convergence results for singularly perturbed Fredholm integrodifferential equation. Journal of Mathematical Analysis 2018; 9 (6): 55-64
  2. Amiraliyev GM, Durmaz ME, Kudu M. Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation. Bulletin of the Belgian Mathematical Society - Simon Stevin 2020; 27 (1): 71-88. doi: 10.36045/bbms/1590199305 [3] Amiraliyev GM, Durmaz ME, Kudu M. A numerical method for a second order singularly perturbed Fredholm integro-differential equation. Miskolc Mathematical Notes 2021; 22 (1): 37-48. doi: 10.18514/MMN.2021.2930 [4] Amiraliyev GM, Mamedov YD. Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations. Turkish Journal of Mathematics 1995; 19: 207-222
  3. Brunner H. Numerical Analysis and Computational Solution of Integro-Differential Equations. Contemporary Computational Mathematics-A Celebration of the 80th Birthday of Ian Sloan (J. Dick et al., eds.) 2018. Springer, Cham: pp. 205-231. doi: 10.1007/978-3-319-72456-0_11 [6] Chen J, He M, Zeng T. A multiscale Galerkin method for second-order boundary value problems of Fredholm integro-differential equation II: Efficient algorithm for the discrete linear system. Journal of Visual Communication and Image Representation 2019; 58: 112-118. doi: 10.1016/j.jvcir.2018.11.027 [7] Chen J, He M, Huang Y. A fast multiscale Galerkin method for solving second order linear Fredholm integrodifferential equation with Dirichlet boundary conditions. Journal of Computational and Applied Mathematics 2020; 364: 112352. doi: 10.1016/j.cam.2019.112352 [8] Dehghan M. Chebyshev finite difference for Fredholm integro-differential equation. International Journal of Computer Mathematics 2008; 85 (1): 123-130. doi: 10.1080/00207160701405436 [9] Doolan ER, Miller JJH, Schilders WHA. Uniform Numerical Methods for Problems with Initial and Boundary Layers. Dublin, Boole Press, 1980
  4. Dönmez Demir D, Lukonde AP, Kürkçü ÖK, Sezer M. Pell–Lucas series approach for a class of Fredholm-type delay integro-differential equations with variable delays. Mathematical Sciences 2021; 15: 55-64. doi: 10.1007/s40096-020- 00370-5 [11] Dzhumabaev DS, Nazarova KZ, Uteshova RE. Modification of the parameterization method for a linear boundary value problem for a Fredholm integro-differential equation. Lobachevskii Journal of Mathematics 2020; 41: 1791- 1800. doi: 10.1134/S1995080220090103 [12]