Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations

Hakkı DURU, (Van Yüzüncü Yıl Üniversitesi, Fen Fakültesi, Matematik Bölümü, Van, Türkiye)
Bahar GÜRBÜZ (Van Yüzüncü Yıl Üniversitesi, Fen Bilimleri Enstitüsü, Matematik Bölümü, Van, Türkiye)
Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi
4 2
Yıl: 2022 Cilt: 27 Sayı: 2 Sayfa Aralığı: 330 - 343 Metin Dili: İngilizce DOI: 10.53433/yyufbed.1085501 İndeks Tarihi: 21-12-2022

Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations

Öz:
In this study, the numerical solution of the singularly perturbed semilinear differential equations with constant delay is investigated by the method of integral identities with use of linear basis functions and interpolating quadrature formulas. The finite difference scheme is established on Boglaev- Bakhvalov type mesh. The error approximations are obtained in the discrete maximum norm. A numerical example is solved to clarify the theoretical analysis.
Anahtar Kelime: Bakhvalov şebeke Düzgün yakınsaklık Fark şeması Singüler pertürbasyon

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık
  • Amiraliyev, G. M., & Mamedov, Y. D. (1995). Difference schemes on the uniform mesh for singularly perturbed pseudo-parabolic equations. Turkish Journal of Mathematics, 19(3), 207-222.
  • Amiraliyev, G. M., & Duru, H. (2003). A uniformly convergent difference method for the periodical boundary value problem. Computers & Mathematics with Applications, 46(5-6), 695-703.
  • Amiraliyev, G. M., & Duru, H. (2005). A note on a parameterized singular perturbation problem. Journal of Computational and Applied Mathematics, 182(1), 233-242.
  • Amiraliyev, G. M., & Cimen, E. (2010). Numerical method for a singularly perturbed convection–diffusion problem with delay. Applied Mathematics and Computation, 216(8), 2351-2359.
  • Amiraliyeva, I. G., Erdogan, F., & Amiraliyev, G. M. (2010). A uniform numerical method for dealing with a singularly perturbed delay initial value problem. Applied Mathematics Letters, 23(10), 1221-1225.
  • Boglaev, I. P. (1984). Approximate solution of a nonlinear boundary value problem with a small parameter for the highest-order differential. USSR Computational Mathematics and Mathematical Physics, 24(6), 30-35.
  • Cakir, M., & Amiraliyev, G. M. (2005). A finite difference method for the singularly perturbed problem with nonlocal boundary condition. Applied Mathematics and Computation, 160(2), 539-549.
  • Doolan, E. R., Miller J. J. H., & Schilders, W. H. A. (1980). Uniform Numerical Methods for Problems with Initial and Boundary Layers. Dublin: Boole Press,.
  • Duru, H., & Gunes, B., (2019). Numerical solutions for singularly perturbed nonlinear reaction diffusion problems on the piecewise equidistant mesh. Erzincan University Journal of Science and Technology, 12 (1), 425-436.
  • Duru, H., & Güneş, B. (2020). The finite difference method on adaptive mesh for singularly perturbed nonlinear 1D reaction diffusion boundary value problems. Journal of Applied Mathematics and Computational Mechanics, 19(4).
  • Erdogan, F., & Amiraliyev, G. M. (2012). Fitted finite difference method for singularly perturbed delay differential equations. Numerical Algorithms, 59(1), 131-145.
  • Erdogan, F., Sakar, M. G., & Saldır, O. (2020). A finite difference method on layer-adapted mesh for singularly perturbed delay differential equations. Applied Mathematics and Nonlinear Sciences, 5(1), 425-436.
  • Farrell, P. A., Hegarty, A. F., Miller, J. J. H., O'Riordan E., & Shishkin, G. I. (2000). Robust Computational Techniques for Boundary Layers. New York : Chapman-Hall/CRC.
  • Gunes, B., Chianeh, A. B., & Demirbas, M., (2020). Comparison of multiple scales method and finite difference method for solving singularly perturbed convection diffusion problem. Gumushane University Journal of Science and Technology Institute, 10(4), 1169-1181.
  • Kumar, S. (2014). Layer-adapted methods for quasilinear singularly perturbed delay differential problems. Applied Mathematics and Computation, 233(1), 214-221.
  • Miller, J. J. H., O'Riordan, E., & Shishkin, G. I. (1996). Fitted Numerical Methods for Singular Perturbation Problems. Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions. Singapore: World Scientific.
  • Roos, H. G., Stynes, M., & Tobiska, L. (1996). Numerical Methods for Singularly Perturbed Differential Equations, Convection-Diffusion and Flow Problems. Berlin: Springer Verlag.
  • Samarski, A. A., (2001). The Theory of Difference Schemes. Moscow, Russia: M.V. Lomonosov State University.
  • Zheng, Q., & Ye, F., (2020). Numerical solution of quasilinear singularly perturbed problems by the principle of equidistribution. Journal of Applied Mathematics and Physics, 8(10), 103603.
APA Duru H, GÜRBÜZ B (2022). Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. , 330 - 343. 10.53433/yyufbed.1085501
Chicago Duru Hakkı,GÜRBÜZ Bahar Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. (2022): 330 - 343. 10.53433/yyufbed.1085501
MLA Duru Hakkı,GÜRBÜZ Bahar Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. , 2022, ss.330 - 343. 10.53433/yyufbed.1085501
AMA Duru H,GÜRBÜZ B Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. . 2022; 330 - 343. 10.53433/yyufbed.1085501
Vancouver Duru H,GÜRBÜZ B Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. . 2022; 330 - 343. 10.53433/yyufbed.1085501
IEEE Duru H,GÜRBÜZ B "Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations." , ss.330 - 343, 2022. 10.53433/yyufbed.1085501
ISNAD Duru, Hakkı - GÜRBÜZ, Bahar. "Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations". (2022), 330-343. https://doi.org/10.53433/yyufbed.1085501
APA Duru H, GÜRBÜZ B (2022). Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27(2), 330 - 343. 10.53433/yyufbed.1085501
Chicago Duru Hakkı,GÜRBÜZ Bahar Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27, no.2 (2022): 330 - 343. 10.53433/yyufbed.1085501
MLA Duru Hakkı,GÜRBÜZ Bahar Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol.27, no.2, 2022, ss.330 - 343. 10.53433/yyufbed.1085501
AMA Duru H,GÜRBÜZ B Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2022; 27(2): 330 - 343. 10.53433/yyufbed.1085501
Vancouver Duru H,GÜRBÜZ B Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations. Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi. 2022; 27(2): 330 - 343. 10.53433/yyufbed.1085501
IEEE Duru H,GÜRBÜZ B "Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations." Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 27, ss.330 - 343, 2022. 10.53433/yyufbed.1085501
ISNAD Duru, Hakkı - GÜRBÜZ, Bahar. "Numerical Solutions of the Singularly Perturbed Semilinear Delay Differential Equations". Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi 27/2 (2022), 330-343. https://doi.org/10.53433/yyufbed.1085501
Sayfa Oluşturulma Tarihi
24-04-2024 4:58

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