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    Wyświetlanie 1-9 z 9
    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:
    Decentralized static output feedback controller design for linear interconnected systems
    Autorzy:
    Fadhilah, Helisyah Nur
    Adzkiya, Dieky
    Arif, Didik Khusnul
    Zhai, Guisheng
    Mardlijah
    Powiązania:
    https://bibliotekanauki.pl/articles/2201019.pdf
    Data publikacji:
    2023
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    output feedback
    decentralized controller
    homotopy method
    interconnected system
    matrix inequality
    sprzężenie zwrotne
    kontroler zdecentralizowany
    metoda homotopii
    system połączony
    nierówność macierzowa
    Opis:
    Many interconnected systems in the real world, such as power systems and chemical processes, are often composed of subsystems. A decentralized controller is suitable for an interconnected system because of its more practical and accessible implementation. We use the homotopy method to compute a decentralized controller. Since the centralized controller constitutes the starting point for the method, its existence becomes very important. This paper introduces a non-singular matrix and a design parameter to generate a centralized controller. If the initial centralized controller fails, we can change the value of the design parameter to generate a new centralized controller. A sufficient condition for a decentralized controller is given as a bilinear matrix inequality with three matrix variables: a controller gain matrix and a pair of other matrix variables. Finally, we present numerical examples to validate the proposed decentralized controller design method.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2023, 33, 1; 83--96
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    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:
    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:
    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:
    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:
    A stable homotopy approach to horizontal linear complementarity problems
    Autorzy:
    Ralph, D.
    Powiązania:
    https://bibliotekanauki.pl/articles/206132.pdf
    Data publikacji:
    2002
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    ciągłość pseudo-Lipschitza
    metoda homotopii
    rozwiązanie stałe
    system kawałkami afiniczny
    active set method
    global metric regularity
    homotopy method
    horizontal linear complementarity problem
    mathematical program with complementarity constraints
    MPCC
    MPCC-LICQ
    MPEC
    path following
    piecewise affine system
    pseudo-Lipschitz continuity
    QPCC
    stable solution
    Opis:
    We are interested in the solution of Horizontal Linear Complementarity Problems, HLCPs, that is complementarity problems with more variables than equations. Globally metrically regular HLCPs have nonempty solution sets that are stable with respect to "right-hand-side perturbations" of the data, hence are numerically attractive. The main purpose of the paper is to show how the stability on conditioning properties of globally metrically regular HLCPs are preserved by a homotopy framework for solving the HLCP that finds a "stable" direcaion at each iteration as a local minimizer of a strongly convex quadratic program with linear complementarity constraints, QPCC. Apart from intrinsic interest in numerical solution of HLCPs, this investigation has application in solving horizontal nonlinear complementarity problems and more broadly in the area of mathematical programs with complementarity constraints, MPCCs.
    Źródło:
    Control and Cybernetics; 2002, 31, 3; 575-599
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    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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