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    Wyświetlanie 1-4 z 4
    Tytuł:
    Approximate solution of painlevé equation i by natural decomposition method and laplace decomposition method
    Autorzy:
    Amir, Muhammad
    Haider, Jamil Abbase
    Ahmad, Shahbaz
    Ashraf, Asifa
    Gul, Sana
    Powiązania:
    https://bibliotekanauki.pl/articles/2233067.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    natural decomposition method
    Laplace decomposition method
    series solution
    Adomain polynomial
    Painlevéequation
    Opis:
    The Painlevé equations and their solutions occur in some areas of theoretical physics, pure and applied mathematics. This paper applies natural decomposition method (NDM) and Laplace decomposition method (LDM) to solve the second-order Painlevé equation. These methods are based on the Adomain polynomial to find the non-linear term in the differential equation. The approximate solution of Painlevé equations is determined in the series form, and recursive relation is used to calculate the remaining components. The results are compared with the existing numerical solutions in the literature to demonstrate the efficiency and validity of the proposed methods. Using these methods, we can properly handle a class of non-linear partial differential equations (NLPDEs) simply. Novelty: One of the key novelties of the Painlevé equations is their remarkable property of having only movable singularities, which means that their solutions do not have any singularities that are fixed in position. This property makes the Painlevé equations particularly useful in the study of non-linear systems, as it allows for the construction of exact solutions in certain cases. Another important feature of the Painlevé equations is their appearance in diverse fields such as statistical mechanics, random matrix theory and soliton theory. This has led to a wide range of applications, including the study of random processes, the dynamics of fluids and the behaviour of non-linear waves.
    Źródło:
    Acta Mechanica et Automatica; 2023, 17, 3; 417--422
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dusty time fractional MHD flow of a Newtonian fluid through a cylindrical tube with a non-Darcian porous medium
    Autorzy:
    Imo-Mani-Singha, H.
    Sengupta, Sanjib
    Powiązania:
    https://bibliotekanauki.pl/articles/1839832.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    time-fractional order Navier-Stokes equation
    Laplace decomposition method
    LDM
    Magnetohydrodynamics
    MHD
    dusty flow
    non-Darcy porous medium
    ciecz newtonowska
    przepływ cieczy nienewtonowskiej
    Laplace Decomposition Method
    magnetohydrodynamika
    Opis:
    In this paper, time fractional flow of a Newtonian fluid through a uniform cylindrical tube with a non-Darcy porous medium in the presence of dust particles under the application of a uniform magnetic field along the meridian axis is discussed. The implication of time fractional order differential equations in flow problems and some benefits of fractional order differential equations are highlighted. The Laplace Decomposition Method (LDM) is used to obtain an approximate solution to the proposed problem. The impact of fractional order and integer order of the differential equations and also the effects of some important parameters on the flow system are shown in the forms of graphs and a table. The convergence test of the solution is done. It has been observed that the fractional order differential equation reveals more things like the decrease in dust particle velocity due to the increase in magnetic field for fractional order derivatives, whereas, no noticeable change in dust particle velocity due to the change in magnetic field for integer order derivatives are observed. Also, it is observed that an increase in a fractional order derivative decrease the fluid as well as the dust particle velocities. The skin friction at the walls of the tube are also highlighted.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 101-114
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Dusty time fractional MHD flow of a Newtonian fluid through a cylindrical tube with a non-Darcian porous medium
    Autorzy:
    Imo-Mani-Singha, H.
    Sengupta, Sanjib
    Powiązania:
    https://bibliotekanauki.pl/articles/1839728.pdf
    Data publikacji:
    2020
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    time-fractional order Navier-Stokes equation
    Laplace decomposition method
    LDM
    Magnetohydrodynamics
    MHD
    dusty flow
    non-Darcy porous medium
    ciecz newtonowska
    przepływ cieczy nienewtonowskiej
    Laplace Decomposition Method
    magnetohydrodynamika
    Opis:
    In this paper, time fractional flow of a Newtonian fluid through a uniform cylindrical tube with a non-Darcy porous medium in the presence of dust particles under the application of a uniform magnetic field along the meridian axis is discussed. The implication of time fractional order differential equations in flow problems and some benefits of fractional order differential equations are highlighted. The Laplace Decomposition Method (LDM) is used to obtain an approximate solution to the proposed problem. The impact of fractional order and integer order of the differential equations and also the effects of some important parameters on the flow system are shown in the forms of graphs and a table. The convergence test of the solution is done. It has been observed that the fractional order differential equation reveals more things like the decrease in dust particle velocity due to the increase in magnetic field for fractional order derivatives, whereas, no noticeable change in dust particle velocity due to the change in magnetic field for integer order derivatives are observed. Also, it is observed that an increase in a fractional order derivative decrease the fluid as well as the dust particle velocities. The skin friction at the walls of the tube are also highlighted.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 4; 101-114
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solution of the modified time fractional coupled burgers equations using laplace adomian decompostion method
    Autorzy:
    Omame, Andrew
    Zaman, Fiazud Din
    Powiązania:
    https://bibliotekanauki.pl/articles/2204660.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    Burgers equations
    fractional derivatives
    Laplace Adomian decomposition method
    semi-analytic solutions
    simulations
    Opis:
    In this work, a coupled system of time-fractional modified Burgers’ equations is considered. Three different fractional operators: Caputo, Caputo-Fabrizio and Atangana-Baleanu operators are implemented for the equations. Also, two different scenarios are examined for each fractional operator: when the initial conditions are u(x,y,0) = sin(xy), v(x,y,0) = sin(xy), and when they are u(x,y,0) = e{−kxy}, v(x,y,0) = e{−kxy}, where k,α are some positive constants. With the aid of computable Adomian polynomials, the solutions are obtained using Laplace Adomian decomposition method (LADM). The method does not need linearization, weak nonlinearity assumptions or perturbation theory. Simulations are also presented to support theoretical results, and the behaviour of the solutions under the three different fractional operators compared.
    Źródło:
    Acta Mechanica et Automatica; 2023, 17, 1; 124--132
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-4 z 4

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