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    Wyświetlanie 1-6 z 6
    Tytuł:
    A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis
    Autorzy:
    Cherniha, R.
    Stachowska-Piętka, J.
    Waniewski, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/907934.pdf
    Data publikacji:
    2014
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    fluid transport
    transport in peritoneal dialysis
    nonlinear partial differential equations
    ordinary differential equation
    steady-state solution
    transport płynu
    dializa otrzewnowa
    nieliniowe równanie różniczkowe
    równanie różniczkowe zwyczajne
    Opis:
    A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a three-component nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations as well as hydrostatic pressure. The model is developed in one spatial dimension approximation, and a governing equation for each of the variables is derived from physical principles. Under some assumptions the model can be simplified to obtain exact formulae for spatially non-uniform steady-state solutions. As a result, the exact formulae for fluid fluxes from blood to the tissue and across the tissue are constructed, together with two linear autonomous ODEs for glucose and albumin concentrations in the tissue. The obtained analytical results are checked for their applicability for the description of fluid-glucose-albumin transport during peritoneal dialysis.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2014, 24, 4; 837-851
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control
    Autorzy:
    Malanowski, K.
    Powiązania:
    https://bibliotekanauki.pl/articles/206654.pdf
    Data publikacji:
    1998
    Wydawca:
    Polska Akademia Nauk. Instytut Badań Systemowych PAN
    Tematy:
    równania różniczkowe nieliniowe
    różniczkowalność rozwiązań
    sterowanie optymalne parametryczne
    differentiability of solutions
    implicit function theorem
    nonlinear ordinary differential equations
    parametric optimal control
    state constraints
    Opis:
    A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).
    Źródło:
    Control and Cybernetics; 1998, 27, 3; 335-352
    0324-8569
    Pojawia się w:
    Control and Cybernetics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Boundary integral solution for a class of fourth-order two-point boundary value problems
    Autorzy:
    Al-Gahtani, H. J.
    Powiązania:
    https://bibliotekanauki.pl/articles/122949.pdf
    Data publikacji:
    2016
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    boundary integral method
    fourth-order differential equation
    nonlinear ordinary differential equations
    nieliniowe równania różniczkowe zwyczajne
    równanie różniczkowe czwartego rzędu
    Opis:
    In this paper, a boundary integral method is proposed for the solution of a class of fourth-order two-boundary value problems described by the equation yiv+P(x, y, y’, y’’, y’’’) = 0, x ∈ ( 0,L), where P is a polynomial function of its arguments. The differential equation is cast in an integral form and the weighted residual technique is used to generate the corresponding boundary integral equations. The boundary integral equations are then, solved by expressing the dependent variable, y, in terms of a power series. The proposed method is tested through four examples to show the applicability of the method to solve a wide range of fourth-order differential equations including the nonlinear ones.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 5-13
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Series Solution of Nonlinear Ordinary Differential Equations Using Single Laplace Transform Method in Mathematical Physics
    Autorzy:
    Mbagwu, JP. C.
    Madububa, B. I.
    Nwamba, J. I.
    Powiązania:
    https://bibliotekanauki.pl/articles/1193352.pdf
    Data publikacji:
    2021
    Wydawca:
    Przedsiębiorstwo Wydawnictw Naukowych Darwin / Scientific Publishing House DARWIN
    Tematy:
    Adomian polynomials
    Single Laplace transform method
    nonlinear ordinary differential equations
    Opis:
    In this paper, a novel technique is created to enable the extension of the single Laplace transform method (SLTM) to solve nonlinear ordinary differential equations (ODEs) is presented. The main parts of the recommended technique are the Adomian polynomials. By developing several theorems, which include the Laplace transformation of nonlinear expressions, the Adomian polynomials are made possible. Several famous nonlinear equations including the Blasius equation, the Poisson Boltzmann equation, and numerous extra problems relating nonlinearities of many types such as exponential and sinusoidal are resolved for description. As it was revealed in the specified equations, and problems, our technique is conceptually and computationally simple. Some nonlinear examples are taken from the literature for checking the validation and convergence of the proposed technique. The suggested method is methodical, precise, then restricted to integration.
    Źródło:
    World Scientific News; 2021, 154; 152-174
    2392-2192
    Pojawia się w:
    World Scientific News
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Variation of parameters method for a three-dimensional problem of condensation film on an inclined rotating disk
    Autorzy:
    Güngör, Osman
    Arslantürk, Cihat
    Powiązania:
    https://bibliotekanauki.pl/articles/122445.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    condensation
    rotating inclined disk
    nonlinear ordinary differential equations
    variation of parameters method
    VPM
    kondensacja
    nieliniowe równania różniczkowe zwyczajne
    metoda zmiany parametrów
    Opis:
    In this paper, the steady three-dimensional problem of condensation film on an inclined rotating disk is considered. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary differential equations system by a similarity transform. The equation system is solved by the variation of parameters method (VPM) which is rather used to solve nonhomogeneous linear differential equations but can also be used to solve nonlinear differential equations. This method has not previously been used to solve a nonlinear condensation problem. The dimensionless velocity and temperature profiles are shown, and the influence of Prandtl number and rotation ratio on the flow field and the Nusselt number are discussed in detail. In order to assess the accuracy of the solutions obtained by this method, the problem is also solved numerically using the Matlab bvp4c solver. The validity of our solutions is verified by the numerical results.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 1; 15-28
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Verified solution method for population epidemiology models with uncertainty
    Autorzy:
    Enszer, J. A.
    Stadtherr, M. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/930132.pdf
    Data publikacji:
    2009
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    dynamika nieliniowa
    epidemiologia
    analiza interwałowa
    równanie różniczkowe
    nonlinear dynamics
    epidemiology
    interval analysis
    verified computing
    ordinary differential equations
    Opis:
    Epidemiological models can be used to study the impact of an infection within a population. These models often involve parameters that are not known with certainty. Using a method for verified solution of nonlinear dynamic models, we can bound the disease trajectories that are possible for given bounds on the uncertain parameters. The method is based on the use of an interval Taylor series to represent dependence on time and the use of Taylor models to represent dependence on uncertain parameters and/or initial conditions. The use of this method in epidemiology is demonstrated using the SIRS model, and other variations of Kermack-McKendrick models, including the case of time-dependent transmission.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2009, 19, 3; 501-512
    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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