Temat: schemat numeryczny - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Uniformly convergent higher-order finite difference scheme for singularly perturbed parabolic problems with non-smUniformly 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
Powiązania:: https://bibliotekanauki.pl/articles/1839851.pdf
Data publikacji:: 2021
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: singularly perturbed parabolic problems
uniformly convergent solution
schemat numeryczny
przepływy konwekcyjno-dyfuzyjne
współczynnik konwekcji
mechanika płynów
Opis:: 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
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 5-16
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Use of partial derivatives to derive a convergent numerical scheme with its error estimates
Autorzy:: Qureshi, Sania
Adeyeye, Oluwaseun
Shaikh, Asif Ali
Powiązania:: https://bibliotekanauki.pl/articles/122734.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: multi-derivative
local truncation error
stability
absolute relative errors
consistency
principal term
wielopochodna
pochodna cząstkowa
schemat numeryczny
błąd względny
błąd bezwzględny
Opis:: Using the idea of the partial derivative with respect to the ordinate of a given mathematical function, a new numerical scheme having third order convergence has been devised for solving initial value problems in ordinary differential equations. Such problems are deemed to be indispensable in diverse fields of science, medical and engineering and are most often required to be solved by the numerical schemes. In view of this, the proposed numerical scheme is found to be efficient in solving both autonomous and non-autonomous type of problems as supported by some numerical experiments in the present study. Using the Taylor expansion for the slopes involved in the scheme, the leading term of the local truncation error is shown to have contained Ϭ(h⁴) which proves third order accuracy of the scheme. In addition to this, consistency and linear stability analysis of the proposed scheme has extensively been discussed. Numerical experiments show better performance of the proposed numerical scheme when compared with existing numerical schemes of the same order as that of the scheme proposed. CPU time (seconds), maximum absolute relative error and the absolute relative error, computed at the last grid point of the integration interval for the associated initial value problem, are the parameters to test the performance of the proposed numerical scheme. MATLAB Version: 9.4.0.813654 (R2018a) in double-precision on a personal computer equipped with a Processor Intel (R) Core(TM) i3-4500U CPU@ 1.70 GHz running under the Windows 10 operating system has been employed in order to carry out all the required numerical computations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 73-83
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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