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Dergiler / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2022 / Cilt: 71 - Sayı: 4

Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers

Muhammet Enes DURMAZ
Musa ÇAKIR
Gabil AMİRALİ
Sayfa
954–967
Yayın Tarihi
2022-12-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The work handles a Fredholm integro-differential equation involving boundary layers.
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Temel Bulgular & Veri:A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions.
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Sonuç & Katkı:The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Finite difference method · Fredholm integro-differential equation · singular perturbation

Abstract

The work handles a Fredholm integro-differential equation involving boundary layers. A fitted second-order difference scheme has been created on a uniform mesh utilizing interpolating quadrature rules and exponential basis functions. The stability and convergence of the proposed discretization technique are analyzed and one example is solved to display the advantages of the presented technique.

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Bu Makaleye Atıf Yap

DURMAZ, M. E., ÇAKIR, M., AMİRALİ, G. (2022). Parameter uniform second-order numerical approximation for the integro-differential equations involving boundary layers. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Cilt: 71 - Sayı: 4, 954–967. https://ajindex.com/articles/867579

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Kaynakça (11)

  1. Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Uniform convergence results for singularly perturbed Fredholm integro-differential equation, J. Math. Anal., 9(6) (2018), 55–64.
  2. Amiraliyev, G. M., Durmaz, M. E., Kudu, M., Fitted second order numerical method for a singularly perturbed Fredholm integro-differential equation, Bull. Belg. Math. Soc. Simon Steven., 27(1) (2020), 71–88. https://doi.org/10.36045/bbms/1590199305
  3. Amiraliyev, G. M., Durmaz, M. E., Kudu, M., A numerical method for a second order singularly perturbed Fredholm integro-differential equation, Miskolc Math. Notes., 22(1) (2021), 37–48. https://doi.org/10.18514/MMN.2021.2930
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  6. Chen, J., He, M., Huang, Y., A fast multiscale Galerkin method for solving second order linear Fredholm integro-differential equation with Dirichlet boundary conditions, J. Comput. Appl. Math., 364 (2020), 112352. https://doi.org/10.1016/j.cam.2019.112352
  7. Dehghan, M., Chebyshev finite difference for Fredholm integro-differential equation, Int. J. Comput. Math., 85 (1) (2008), 123–130. https://doi.org/10.1080/00207160701405436
  8. Doolan, E. R., Miller, J. J. H., Schilders, W. H. A., Uniform Numerical Methods for Problems with Initial and Boundary Layers, Boole Press, Dublin, 1980.
  9. Durmaz, M. E., Amiraliyev, G. M., A robust numerical method for a singularly perturbed Fredholm integro-differential equation, Mediterr. J. Math., 18(24) (2021), 1–17. https://doi.org/10.1007/s00009-020-01693-2
  10. Durmaz, M. E., Amiraliyev, G. M., Kudu, M., Numerical solution of a singularly perturbed Fredholm integro differential equation with Robin boundary condition, Turk. J. Math., 46(1) (2022), 207–224. https://doi.org/10.3906/mat-2109-11
  11. Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O’Riordan, E., Shishkin, G. I., Robust Comput