Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smooth data

• Autorzy: Bullo Tesfaye Aga , Degla Guy Aymard , Duressa Gemechis File

Identyfikatory

DOI

10.17512/jamcm.2021.1.01

• Języki publikacji: EN

Abstrakty

EN

A uniformly convergent higher-order finite difference scheme is constructed and analyzed for solving singularly perturbed parabolic problems with non-smooth data. This scheme involves an average non-standard finite difference with the Richardson extrapolation method for space variables and second-order finite difference approximation for time direction on uniform meshes. The scheme is shown to be second-order convergent in both temporal and spatial directions. Further, the scheme is proven to be uniformly convergent and also confirmed by numerical experiments. Wide numerical experiments are conducted to support the theoretical results and to demonstrate its accuracy. Concisely, the present scheme is stable, convergent, and more accurate than existing methods in the literatur

Słowa kluczowe

EN

singularly perturbed parabolic problems; uniformly convergent solution

PL

schemat numeryczny; przepływy konwekcyjno-dyfuzyjne; współczynnik konwekcji; mechanika płynów

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2021
• Tom: Vol. 20, nr 1
• Strony: 5--16
• Opis fizyczny: Bibliogr. 19 poz. rys., tab.

Twórcy

autor

Bullo Tesfaye Aga

• Department of Mathematics, Jimma University, Jimma, Ethiopia

autor

Degla Guy Aymard

• Institut De Mathematiques et de sciences physiques, Universit D'Abomey Calavi, Benin

autor

Duressa Gemechis File

• Department of Mathematics, Jimma University, Jimma, Ethiopia

Bibliografia

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• [6] Jha, A., & Kadalbajoo, M.K. (2015). A robust layer adapted difference method for singularly perturbed two-parameter parabolic problems. International Journal of Computer Mathematics, 92, 1204-1221.
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• [10] Mukherjee, K., & Natesan, S. (2011). Optimal error estimate of the upwind scheme on Shishkintype meshes for singularly perturbed parabolic problems with discontinuous convection coefficients. BIT Numerical Mathematics, 51, 289-315, DOI: 10.1007/s10543-010-0292-2.
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• [12] Tesfaye, A.B., Gemechis, F.D., & Degla, G.A. (2020). Robust finite difference method for singularly perturbed two-parameter parabolic convection-diffusion problems. International Journal of Computational Methods, DOI: 10.1142/S0219876220500346.
• [13] Munyakazi, J.B. (2015). A robust finite difference method for two-parameter parabolic convection-diffusion problems. An International Journal of Applied Mathematics and Information Sciences, 9, 2877-2883.
• [14] Munyakazi, J.B., & Patidar, K.C. (2013). A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems. Computational and Applied Mathematics, 32, 509-519.
• [15] Munyakazi, J.B., Patidar, K.C., & Mbani, T.S. (2019). A fitted numerical method for parabolic turning point singularly perturbed problems with an interior layer. Numerical Methods for Partial Differential Equations, 35, 2407-2422.
• [16] O’Riordan, E., & Shishkin, G.I. (2004). Singularly perturbed parabolic problems with non-smooth data. Journal of Computational and Applied Mathematics, 166, 233-245.
• [17] Rajan, M.P., & Reddy, G.D. (2015). An iterative technique for solving singularly perturbed parabolic PDE. Journal of Applied Mathematics and Computing, DOI: 10.1007/s12190-015-0866-x.
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• [19] Tesfaye, A.B., Gemechis, F.D., & Degla, G.A. (2019). Higher-order fitted operator finite difference method for two-parameter parabolic convection-diffusion problems. International Journal of Engineering and Applied Sciences (IJEAS), 11, 455-467.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).