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    Wyświetlanie 1-6 z 6
    Tytuł:
    Numerical solutions to integral equations equivalent to differential equations with fractional time
    Autorzy:
    Bandrowski, B.
    Karczewska, A.
    Rozmej, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/907763.pdf
    Data publikacji:
    2010
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    równanie ułamkowe
    metoda Galerkina
    dyfuzja anomalna
    fractional equations
    Galerkin method
    anomalous diffusion
    Opis:
    This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2010, 20, 2; 261-269
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Strouhal number effects on dynamic boundary layer evolution over a wedge surface from initial flow to steady flow: analytical approach
    Autorzy:
    Bachiri, Mohamed
    Bouabdallah, Ahcen
    Powiązania:
    https://bibliotekanauki.pl/articles/27312409.pdf
    Data publikacji:
    2022
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    liczba Strouhala
    dyfuzja
    konwekcja
    unsteady boundary layer
    wedge surface
    Strouhal number
    superposition method
    diffusion
    convective
    Opis:
    The present work studies the effects of the physical parameter characterizing the laminar flow regime, namely the Strouhal number, on the evolution of the unsteady dynamic boundary-layer developed along a wedge surface. Similarity method is used to transform unsteady momentum equation to dimensionless form. Using superposition method between diffusion and convective flows solutions, an ad hoc velocity profile formula is proposed. The obtained results confirm perfectly the numerical data given by Blasius, Falkner-Skan and Williams-Rhyne for all Strouhal numbers. A new accurate analytical function of the local skin friction is established for all time values and for different wedge surface directions. In order to give further clarification on the flows evolutions from diffusion flow to convective flow, in the whole space domain, new skin friction coefficient curves are plotted for all Strouhal numbers and for different wedge surface directions.
    Źródło:
    International Journal of Applied Mechanics and Engineering; 2022, 27, 4; 26--39
    1734-4492
    2353-9003
    Pojawia się w:
    International Journal of Applied Mechanics and Engineering
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Finite-Dimensional Control of Nonlinear Parabolic Pde Systems With Time-Dependent Spatial Domains Using Empirical Eigenfunctions
    Autorzy:
    Armaou, A.
    Christofides, P. D.
    Powiązania:
    https://bibliotekanauki.pl/articles/908332.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    sterowanie nieliniowe
    sterowanie skończenie wymiarowe
    Karhunen-Loeve expansion
    Galerkin's method
    nonlinear control
    diffusion-reaction processes with moving boundaries
    Opis:
    This article presents a methodology for the synthesis of finite-dimensional nonlinear output feedback controllers for nonlinear parabolic partial differential equation (PDE) systems with time-dependent spatial domains. Initially, the nonlinear parabolic PDE system is expressed with respect to an appropriate time-invariant spatial coordinate, and a representative (with respect to different initial conditions and input perturbations) ensemble of solutions of the resulting time-varying PDE system is constructed by computing and solving a high-order discretization of the PDE. Then, the Karhunen-Loeve expansion is directly applied to the ensemble of solutions to derive a small set of empirical eigenfunctions (dominant spatial patterns) that capture almost all the energy of the ensemble of solutions. The empirical eigenfunctions are subsequently used as basis functions within a Galerkin model reduction framework to derive low-order ordinary differential equation (ODE) systems that accurately describe the dominant dynamics of the PDE system. The ODE systems are subsequently used for the synthesis of nonlinear output feedback controllers using geometric control methods. The proposed control method is used to stabilize an unstable steady-state of a diffusion-reaction process with nonlinearities, spatially-varying coefficients and time-dependent spatial domain, and is shown to lead to the construction of accurate low-order models and the synthesis of low-order controllers. The performance of the low-order models and controllers is successfully tested through computer simulations.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 2; 287-317
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method
    Autorzy:
    Sun, Kaiyue
    Liu, Xiangyang
    Powiązania:
    https://bibliotekanauki.pl/articles/1838202.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    autonomous underwater vehicle
    path planning
    heat method
    heat diffusion
    cost function
    autonomiczny pojazd podwodny
    planowanie trasy
    dyfuzja ciepła
    funkcja kosztu
    Opis:
    This paper proposes a novel autonomous underwater vehicle path planning algorithm in a cluttered underwater environment based on the heat method. The algorithm calculates the isotropic and anisotropic geodesic distances by adding the direction and magnitude of the currents to the heat method, which is named the anisotropy-based heat method. Taking account of the relevant influence of the environment on the cost functions, such as currents, obstacles and turn of the vehicle, an efficient collision-free and energy-optimized path solution can be obtained. Simulation results show that the anisotropy-based heat method is able to find a good trajectory in both static and dynamic clutter fields (including uncertain obstacles and changing currents). Compared with the fast marching (FM) algorithm, the anisotropy-based heat method is not only robust, flexible, and simple to implement, but it also greatly saves time consumption and memory footprint in a time-variant environment. Finally, the evaluation criteria of paths are proposed in terms of length, arrival time, energy consumption, and smoothness.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 289-301
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Path planning for an autonomous underwater vehicle in a cluttered underwater environment based on the heat method
    Autorzy:
    Sun, Kaiyue
    Liu, Xiangyang
    Powiązania:
    https://bibliotekanauki.pl/articles/1838198.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    autonomous underwater vehicle
    path planning
    heat method
    heat diffusion
    cost function
    pojazd podwodny autonomiczny
    planowanie trasy
    dyfuzja ciepła
    funkcja kosztu
    Opis:
    This paper proposes a novel autonomous underwater vehicle path planning algorithm in a cluttered underwater environment based on the heat method. The algorithm calculates the isotropic and anisotropic geodesic distances by adding the direction and magnitude of the currents to the heat method, which is named the anisotropy-based heat method. Taking account of the relevant influence of the environment on the cost functions, such as currents, obstacles and turn of the vehicle, an efficient collision-free and energy-optimized path solution can be obtained. Simulation results show that the anisotropy-based heat method is able to find a good trajectory in both static and dynamic clutter fields (including uncertain obstacles and changing currents). Compared with the fast marching (FM) algorithm, the anisotropy-based heat method is not only robust, flexible, and simple to implement, but it also greatly saves time consumption and memory footprint in a time-variant environment. Finally, the evaluation criteria of paths are proposed in terms of length, arrival time, energy consumption, and smoothness.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 289-301
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A conservative scheme with optimal error estimates for a multidimensional space-fractional Gross–Pitaevskii equation
    Autorzy:
    Hendy, Ahmed S.
    Macías-Díaz, Jorge E.
    Powiązania:
    https://bibliotekanauki.pl/articles/330834.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    generalized Gross–Pitaevskii system
    Riesz fractional diffusion
    Sobolev inequality
    conservative method
    optimal error bounds
    równanie Grossa-Pitaevskiego
    nierówność Sobolewa
    metoda konserwatywna
    optymalna granica błędu
    Opis:
    The present work departs from an extended form of the classical multi-dimensional Gross–Pitaevskii equation, which considers fractional derivatives of the Riesz type in space, a generalized potential function and angular momentum rotation. It is well known that the classical system possesses functionals which are preserved throughout time. It is easy to check that the generalized fractional model considered in this work also possesses conserved quantities, whence the development of conservative and efficient numerical schemes is pragmatically justified. Motivated by these facts, we propose a finite-difference method based on weighted-shifted Grünwald differences to approximate the solutions of the generalized Gross–Pitaevskii system. We provide here a discrete extension of the uniform Sobolev inequality to multiple dimensions, and show that the proposed method is capable of preserving discrete forms of the mass and the energy of the model. Moreover, we establish thoroughly the stability and the convergence of the technique, and provide some illustrative simulations to show that the method is capable of preserving the total mass and the total energy of the generalized system.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 4; 713-723
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-6 z 6

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