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    Wyświetlanie 1-9 z 9
    Tytuł:
    The homotopy analysis Rangaig transform method for nonlinear partial differential equations
    Autorzy:
    Ziane, Djelloul
    Cherif, Mountassir Hamdi
    Powiązania:
    https://bibliotekanauki.pl/articles/2175522.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    Rangaig transform method
    homotopy analysis method
    nonlinear partial differential equations
    metoda transformacji Rangaiga
    metoda analizy homotopii
    nieliniowe równania różniczkowe cząstkowe
    Opis:
    The idea suggested in this article is to combine the Rangaig transform with the homotopy analysis method in order to facilitate the solution of nonlinear partial differentia equations. This method may be called the homotopy analysis Rangaig transform method (HARTM). The proposed example results showed that HARTM is an effective method for solving nonlinear partial differential equations.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 2; 111--122
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Thermal performance of porous fins with temperature-dependent heat generation via the homotopy perturbation method and collocation method
    Autorzy:
    Hoshyar, H. A.
    Rahimipetroudi, I.
    Ganji, D. D.
    Majidian, A. R.
    Powiązania:
    https://bibliotekanauki.pl/articles/122933.pdf
    Data publikacji:
    2015
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    collocation method
    homotopy perturbation method
    porous fin
    temperature-dependent heat generation
    Opis:
    An analysis has been performed to study the problem of the thermal performance of a nonlinear problem of the porous fin with temperature-dependent internal heat generation. Highly accurate semi-analytical methods called the collocation method (CM) and the homotopy perturbation method (HPM) are introduced and then are used to obtain a nonlinear temperature distribution equation in a longitudinal porous fin. This study is performed using passage velocity from the Darcy’s model to formulate the heat transfer equation through porous media. The heat generation is assumed to be a function of temperature. The effects of the natural convection parameter Nc, internal heat generation εg, porosity Sh and generation number G parameter on the dimensionless temperature distribution are discussed. Also, numerical calculations called the fourth order Runge-Kutta method were carried out for the various parameters entering into the problem for validation. Results reveal that analytical approaches are very effective and convenient. Also it is found that these methods can achieve more suitable results compared to numerical methods.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2015, 14, 4; 53-65
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Homotopy perturbation Shehu transform method for solving fractional models arising in applied sciences
    Autorzy:
    Maitama, Shehu
    Zhao, Weidong
    Powiązania:
    https://bibliotekanauki.pl/articles/1839856.pdf
    Data publikacji:
    2021
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    homotopy perturbation technique
    Shehu transform
    numeric computations
    symbolic computations
    fractional model
    metoda transformacji Shehu
    model ułamkowy
    obliczenia numeryczne
    obliczenia symboliczne
    technika homotopii
    metoda perturbacji homotopii
    Opis:
    Using the recently proposed homotopy perturbation Shehu transform method (HPSTM), we successfully construct reliable solutions of some important fractional models arising in applied physical sciences. The nonlinear terms are decomposed using He’s polynomials, and the fractional derivative is calculated in the Caputo sense. Using the analytical method, we obtained the exact solution of the fractional diffusion equation, fractional wave equation and the nonlinear fractional gas dynamic equation.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 1; 71-82
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Heat transfer analysis of non-Newtonian natural convective fluid flow using Homotopy Perturbation and Daftardar-Gejiji & Jafari Methods
    Autorzy:
    Adeleye, Olurotimi
    Yinusa, Ahmed
    Powiązania:
    https://bibliotekanauki.pl/articles/122431.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    non-Newtonian fluid
    natural convection
    vertically infinite plates
    Daftardar-Gejiji & Jafari Method
    DJM
    Homotopy Perturbation Method
    HPM
    ciecz nieniutonowska
    konwekcja naturalna
    metoda Daftardar-Gejiji i Jafari
    metoda perturbacji homotopii
    Opis:
    In this paper, the analytical solution of natural convective heat transfer of a non-Newtonian fluid flow between two vertical infinite plates using the Homotopy Perturbation Method (HPM) and Daftardar-Gejiji & Jafari Method (DJM) is presented. The heat transfer problem of natural convection is observed in many engineering fields including geothermal systems, heat exchangers, petroleum reservoirs, nuclear waste reserves, etc. The problem which is modelled as fully coupled nonlinear ordinary differential equations requires special analytical techniques for its solution. The solutions are obtained using an exact analytical method: the Homotopy Perturbation Method (HPM) and a semi-analytical method: the Daftardar-Gejiji & Jafari Method (DJM). These solutions are compared with solutions obtained from the Runge-Kutta numerical method. The results are in good agreement with the numerical solutions. The effects of the Eckert number, Prandtl number and the non-Newtonian fluid viscosity parameter on the non-dimensional temperature and velocity of the fluid are investigated. The results obtained from the analytical method show that the method can be applied to predict excellent results of the problem and can be used for parametric studies of the problem. From the results, it is shown that when the Prandtl number and the Eckert number are increased, there is an increase in both temperature and fluid flow velocity.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 5-18
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Spectral-homotopy analysis of MHD non-orthogonal stagnation point flow of a nanofluid
    Autorzy:
    Chaharborj, S.
    Moameni, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/122375.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nanofluid
    MHD stagnation flow
    stretching sheet
    SHAM
    metoda analizy homotopii spektralnej
    Opis:
    In this article, we investigate the theoretical study of the magnetohy-drodynamic (MHD) non-orthogonal stagnation point flow of a nanofluid towards a stretching. The partial differential equations that model the problem are reduced to ordinary differential equations which are then solved analytically using the improved Spectral Homotopy Analysis Method (SHAM). Comparisons of our results from SHAM and numerical solutions show that this method is a capable tool for solving this type of linear and nonlinear problems semi-analytically.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 1; 15-28
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    On the semi-analytic technique to deal with nonlinear fractional differential equations
    Autorzy:
    Khirsariya, Sagar R.
    Rao, Snehal B.
    Powiązania:
    https://bibliotekanauki.pl/articles/2202059.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    fractional differential equation
    logistic equation
    Fornberg-Whitham equation
    homotopy perturbation method
    Sawi transform
    ułamkowe równanie różniczkowe
    równanie logistyczne
    równanie Fornberga-Whithama
    metoda perturbacji homotopii
    Opis:
    In this article, we present a novel hybrid approach, by combining the Sawi transform with the homotopy perturbation method, to achieve the approximate and analytic solutions of nonlinear fractional differential equations (ODE as well as PDE) using the time-fractional Caputo derivative. The proposed algorithm is faster and simple compared to other iterative methods. The Sawi transform is used along with the homotopy perturbation method to accelerate the convergence of the series solution. The results discussed using calculations, graphs and tables are compatible for comparison with other known methods like the residual power series method and the exact solution which are discussed in the literature.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 1; 17--30
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical scheme methods for solving nonlinear pseudo-hyperbolic partial differential equations
    Autorzy:
    Abdulazeez, Sadeq Taha
    Modanli, Mahmut
    Husien, Ahmad Muhamad
    Powiązania:
    https://bibliotekanauki.pl/articles/2202054.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear pseudo-hyperbolic partial differential equation
    homotopy analysis method
    variational iteration method
    approximate solution
    nieliniowe pseudohiperboliczne równanie różniczkowe cząstkowe
    homotopijna metoda analizy
    metoda iteracji wariacyjnych
    rozwiązanie przybliżone
    Opis:
    The numerical solutions to the nonlinear pseudo-hyperbolic partial differentia equation with nonlocal conditions are presented in this study. This equation is solved using the homotopy analysis technique (HAM) and the variational iteration method (VIM). Both strategies are compared and contrasted in terms of approximate and accurate solutions. The results show that the HAM technique is more appropriate, effective, and close to the exact solution than the VIM method. Finally, the graphical representations of the obtained results are given.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 4; 5--15
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    The stability conditions of the cubic damping Van der Pol-Duffing oscillator using the HPM with the frequency-expansion technology
    Autorzy:
    El-Dib, Y. O.
    Powiązania:
    https://bibliotekanauki.pl/articles/122293.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    homotopy perturbation method
    nonlinear oscillators
    cubic nonlinear damping van der Pol’s equation
    nonlinear frequency analysis
    stability analysis
    metoda perturbacji homotopii
    HPM
    homotopijna metoda perturbacyjna
    oscylator Van der Pol-Duffing
    analiza stabilności
    teoria perturbacji
    oscylator nieliniowy
    analiza częstotliwościowa
    Opis:
    In this paper, we perform the frequency-expansion formula for the nonlinear cubic damping van der Pol’s equation, and the nonlinear frequency is derived. Stability conditions are performed, for the first time ever, by the nonlinear frequency technology and for the nonlinear oscillator. In terms of the van der Pol’s coefficients the stability conditions have been performed. Further, the stability conditions are performed in the case of the complex damping coefficients. Moreover, the study has been extended to include the influence of a forcing van der Pol’ oscillator. Stability conditions have been derived at each resonance case. Redoing the perturbation theory for the van der Pol oscillator illustrates more of a resonance formulation such as sub-harmonic resonance and super-harmonic resonance. More approximate nonlinear dispersion relations of quartic and quintic forms in the squaring of the extended frequency are derived, respectively.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 3; 31-44
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Solutions of Benjamin-Bona-Mahony, modified Camassa-Holm and Degasperis Procesi equations using an iterative method
    Autorzy:
    Kumar, Manoj
    Powiązania:
    https://bibliotekanauki.pl/articles/2202030.pdf
    Data publikacji:
    2022
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    nonlinear Bejamin-Bona-Mahony equation
    modified Camassa-Holm equation
    modified Degasperis-Procesi equation
    Daftardar-Gejji and Jafari method
    homotopy perturbation method
    Adomian decomposition method
    nieliniowe równanie Bejamina-Bony-Mahony'ego
    zmodyfikowane równanie Camassy-Holma
    zmodyfikowane równanie Degasperisa-Procesiego
    metoda Daftardara-Gejji i Jafari
    metoda perturbacji homotopii
    metoda dekompozycji Adomiana
    Opis:
    In the present paper, we solve the non-linear Benjamin-Bona-Mahony, modified Camassa-Holm, and Degasperis-Procesi equations using an iterative method introduced by Daftardar-Gejji and Jafari. Results are compared with those obtained by other iterative methods such as the Adomian decomposition method and homotopy perturbation method. It is observed that the proposed method is computationally inexpensive and yields more accurate solutions than the Adomian decomposition method and the homotopy perturbation method.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2022, 21, 3; 59--72
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-9 z 9

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