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    Wyświetlanie 1-5 z 5
    Tytuł:
    On Granular Derivatives and the Solution of a Granular Initial Value Problem
    Autorzy:
    Batyrshin, I.
    Powiązania:
    https://bibliotekanauki.pl/articles/908040.pdf
    Data publikacji:
    2002
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    informatyka
    fuzzy differential
    fuzzy granule
    initial value problem
    cylindrical extension
    Opis:
    Perceptions about function changes are represented by rules like "If X is SMALL then Y is QUICKLY INCREASING." The consequent part of a rule describes a granule of directions of the function change when X is increasing on the fuzzy interval given in the antecedent part of the rule. Each rule defines a granular differential and a rule base defines a granular derivative. A reconstruction of a fuzzy function given by the granular derivative and the initial value given by the rule is similar to Euler's piecewise linear solution of an initial value problem. The solution method is based on a granulation of the directions of the function change, on an extension of the initial value in directions and on a propagation of fuzzy constraints given in antecedent parts of rules on possible function values. The proposed method is illustrated with an example.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2002, 12, 3; 403-410
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A verified method for solving piecewise smooth initial value problems
    Autorzy:
    Auer, E.
    Kiel, S.
    Rauh, A.
    Powiązania:
    https://bibliotekanauki.pl/articles/331354.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    interval method
    non smooth system
    initial value problem
    metoda przedziałowa
    metoda nie gładka
    zagadnienie początkowe
    Opis:
    In many applications, there is a need to choose mathematical models that depend on non-smooth functions. The task of simulation becomes especially difficult if such functions appear on the right-hand side of an initial value problem. Moreover, solution processes from usual numerics are sensitive to roundoff errors so that verified analysis might be more useful if a guarantee of correctness is required or if the system model is influenced by uncertainty. In this paper, we provide a short overview of possibilities to formulate non-smooth problems and point out connections between the traditional non-smooth theory and interval analysis. Moreover, we summarize already existing verified methods for solving initial value problems with non-smooth (in fact, even not absolutely continuous) right-hand sides and propose a way of handling a certain practically relevant subclass of such systems. We implement the approach for the solver VALENCIA-IVP by introducing into it a specialized template for enclosing the first-order derivatives of non-smooth functions. We demonstrate the applicability of our technique using a mechanical system model with friction and hysteresis. We conclude the paper by giving a perspective on future research directions in this area.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 4; 731-747
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A mixed type boundary-value problem related to the electrostatics of cold plasma jet reactors based on dielectric barrier discharge
    Autorzy:
    Vafeas, Panayiotis
    Papadopoulos, Polycarpos K.
    Svarnas, Panagiotis
    Powiązania:
    https://bibliotekanauki.pl/articles/1838214.pdf
    Data publikacji:
    2021
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    DBD
    dielectric barrier discharge
    cold plasma jet
    reactor
    mixed type boundary value problem
    electrostatic potential theory
    Opis:
    A semi-analytical model is presented for the determination of the electric field in reactors used for cold atmospheric pressure plasma (CAPP) jet production, based on the concept of dielectric barrier discharge (DBD). These systems are associated with various applications in contemporary engineering, ranging from material processing to biomedicine, and at the same time they provide many challenges for fundamental research. Here, we consider a simplified system configuration of a single driven electrode, surrounding a thin dielectric tube, which does not contribute to the electric field, since the potential variation is immediate due to its negligible size. By employing the cylindrical coordinate system that perfectly fits the present plasma jet reactor, we separate the area of electric activity into three distinct domains according to the imposed external conditions, while our analysis is restricted to the electrostatic limit of Maxwell’s equations. To this end, cylindrical harmonic field expansions are used for the potential, which produce the corresponding electric fields in each subdomain. Due to the imposed mixed-type boundary value problem, additional linear terms are incorporated, leading to three possible analytical solutions of the physical problem under consideration. The efficiency of the method is demonstrated by comparing the final formulae with a numerical solution, followed by the relevant discussion.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2021, 31, 2; 233-245
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An Algorithm for Construction of varepsilon-Value Functions for the Bolza Control Problem
    Autorzy:
    Jacewicz, E.
    Powiązania:
    https://bibliotekanauki.pl/articles/908335.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja nieliniowa
    sterowanie optymalne
    nonlinear optimization
    Bolza problem
    optimal control
    Hamilton-Jacobi equation
    dynamic programming
    varepsilon-value function
    approximate minimum
    Opis:
    The problem considered is that of approximate numerical minimisation of the non-linear control problem of Bolza. Starting from the classical dynamic programming method of Bellman, an varepsilon-value function is defined as an approximation for the value function being a solution to the Hamilton-Jacobi equation. The paper shows how an varepsilon-value function which maintains suitable properties analogous to the original Hamilton-Jacobi value function can be constructed using a stable numerical algorithm. The paper shows the numerical closeness of the approximate minimum to the infimum of the Bolza functional.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 2; 391-428
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A Method for Constructing ε-value Functions for The Bolza Problem of Optimal Control
    Autorzy:
    Pustelnik, J.
    Powiązania:
    https://bibliotekanauki.pl/articles/911140.pdf
    Data publikacji:
    2005
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    optymalizacja nieliniowa
    sterowanie optymalne
    równanie Hamiltona-Jacobiego
    programowanie dynamiczne
    wartość funkcji
    nonlinear optimization
    Bolza problem
    optimal control
    Hamilton-Jacobi equation
    dynamic programming
    value function
    approximate minimum
    Opis:
    The problem considered is that of approximate minimisation of the Bolza problem of optimal control. Starting from Bellman's method of dynamic programming, we define the ε-value function to be an approximation to the value function being a solution to the Hamilton-Jacobi equation. The paper shows an approach that can be used to construct an algorithm for calculating the values of an ε-value function at given points, thus approximating the respective values of the value function.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2005, 15, 2; 177-186
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
      Wyświetlanie 1-5 z 5

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