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Wyświetlanie 1-4 z 4
Tytuł:
Comparative analysis of Riemann-Liouville, Caputo-Fabrizio, and Atangana-Baleanu integrals
Autorzy:
Shaikh, Asif Ali
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/2175503.pdf
Data publikacji:
2022
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
fractional operator
gamma function
absolute error
convergence
operator ułamkowy
funkcja gamma
błąd bezwzględny
konwergencja
Opis:
This study analyzes the most commonly used operators of the Riemann-Liouville, the Caputo-Fabrizio, and the Atangana-Baleanu integral operators. Firstly, a numerical scheme for the Riemann-Liouville fractional integral has been discussed. Then, two numerical techniques have been suggested for the remaining two operators. The experimental order of convergence for the schemes is further supported by the computations of absolute relative error at the final nodal point over the integration interval [0, T ]. Comparative analysis of the integrals reveals that the Riemann-Liouville fractional integral yields the most minor errors and the most significant experimental order of convergence in the majority of functions, particularly when the fractional-order parameter α → 0. It is worth noting that the Atangana-Baleanu has proved to be an essential operator for solving many dynamical systems that a single RL operator cannot handle. All of the three integral operators coincide with each other for α = 1. Mathematica 11.3 for an Intel(R) Core(TM) i3-4500U procesor running on 1.70 GHz is used to carry out all the necessary computations.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 1; 91--101
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
A new nonlinear L-stable scheme with constant and adaptive step-size strategy
Autorzy:
Arain, Sadia
Qureshi, Sania
Shaikh, Asif Ali
Powiązania:
https://bibliotekanauki.pl/articles/2175496.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
stiff systems
singular systems
L-stability
local error
order stars
systemy sztywne
układ singularny
stabilność L
błąd lokalny
Opis:
The present study proposes a new explicit nonlinear scheme that solves stiff and nonlinear initial value problems in ordinary differential equations. One of the promising features of this scheme is its fourth-order convergence with strong stability having an unbounded region. A modern approach for relative stability growth analysis is also presented under order stars conditions. The scheme is also good in dealing with singular and stiff type of models. Comparing numerical experiments using various errors, including maximum absolute global error over the integration interval, absolute error at the endpoint, average error, norm of errors, and the CPU times (seconds), shows better performance. An adaptive step-size approach seems to increase the performance of the proposed scheme. The numerical simulations assure us of L -stability, consistency, order, and rapid convergence.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 7--18
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
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
Artykuł
Tytuł:
Comparative analysis of numerical simulations of blood flow through the segment of an artery in the presence of stenosis
Autorzy:
Shaikh, Fozia
Shaikh, Asif Ali
Hincal, Evren
Qureshi, Sania
Powiązania:
https://bibliotekanauki.pl/articles/24201504.pdf
Data publikacji:
2023
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
incompressible
isothermal
blood flow
stenosis
finite element method
izotermiczność
przepływ krwi
zwężenie
metoda elementów skończonych
Opis:
A mathematical model is developed to study the characteristics of blood flowing through an arterial segment in the presence of a single and a couple of stenoses. The governing equations accompanied by an appropriate choice of initial and boundary conditions are solved numerically by Taylor Galerkin’s time-stepping equation, and the numerical stability is checked. The pressure, velocity, and stream functions have been solved by Cholesky’s method. Furthermore, an in-depth study of the flow pattern reveals the separation of Reynolds number for the 30 and 50% blockage of single stenosis and 30% blockage of multi-stenosis. The present results predict the excess pressure drop across the stenosis site than it does for the inlet of the artery with single and multiple stenosis and the increase in the velocity is observed at the center of the artery.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 49--61
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
    Wyświetlanie 1-4 z 4

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