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    Wyświetlanie 1-3 z 3
    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:
    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
    Tytuł:
    Solution of fractional heat-like and fractional wave-like equation by using modern strategy
    Autorzy:
    Mohamed, Zain El Abden
    Hamza, Amjad
    Elzaki, Tarig
    Algolam, Mohamed
    Elhussein, Shiraz
    Powiązania:
    https://bibliotekanauki.pl/articles/2233715.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Białostocka. Oficyna Wydawnicza Politechniki Białostockiej
    Tematy:
    fractional-order wave-like equation
    fractional-order heat-like equation
    initial-boundary value problem
    Adomian decomposition method
    Opis:
    This paper introduces a novel form of the Adomian decomposition (ADM) method for solving fractional-order heat-like and wave-like equations with starting and boundary value problems. The derivations are provided in the sense of Caputo. In order to help understanding, the generalised formulation of the current approach is provided. Several numerical examples of fractional-order diffusion-wave equations (FDWEs) are solved using the suggested method in this context. In addition to examining the applicability of the suggested method to the solving of fractional-order heat-like and wave-like equations, a graphical depiction of the solutions to three instructive cases was constructed. Solution graphs were arrived at for integer and fractional-order problems. The derived and exact solutions to integer-order problems were found to be in excellent agreement. The subject of the present research endeavour is the convergence of fractional-order solutions. This strategy is considered to be the most successful way of addressing fractional-order initial-boundary value issues in science and engineering. This strategy is presented here.
    Źródło:
    Acta Mechanica et Automatica; 2023, 17, 3; 372--380
    1898-4088
    2300-5319
    Pojawia się w:
    Acta Mechanica et Automatica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-3 z 3

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