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    Wyświetlanie 1-10 z 10
    Tytuł:
    A posteriori error estimates for beams with inexact flexural stiffness representation
    Autorzy:
    Torii, André J.
    Gracite, Paula M.A.
    Miguel, Leandro F.F.
    Lopez, Rafael H.
    Powiązania:
    https://bibliotekanauki.pl/articles/24201505.pdf
    Data publikacji:
    2023
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    beam
    error estimate
    inexact stiffness
    belka
    oszacowanie błędów
    Opis:
    In this work, we present a posteriori error estimates for the Euler-Bernoulli beam theory with inexact flexural stiffness representation. This is an important subject in practice because beams with non-uniform flexural stiffness are frequently modeled using a mesh of elements with constant stiffness. The error estimates obtained in this work are validated by means of two numerical examples. The estimates presented here can be employed for adaptive mesh refinement.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2023, 22, 2; 62--74
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Bernstein operational matrix of differentiation and collocation approach for a class of three-point singular BVPs: error estimate and convergence analysis
    Autorzy:
    Sriwastav, Nikhil
    Barnwal, Amit K.
    Wazwaz, Abdul-Majid
    Singh, Mehakpreet
    Powiązania:
    https://bibliotekanauki.pl/articles/29519371.pdf
    Data publikacji:
    2023
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    Bernstein polynomials
    collocation method
    three-point singular BVPs
    convergence analysis
    error estimate
    Opis:
    Singular boundary value problems (BVPs) have widespread applications in the field of engineering, chemical science, astrophysics and mathematical biology. Finding an approximate solution to a problem with both singularity and non-linearity is highly challenging. The goal of the current study is to establish a numerical approach for dealing with problems involving three-point boundary conditions. The Bernstein polynomials and collocation nodes of a domain are used for developing the proposed numerical approach. The straightforward mathematical formulation and easy to code, makes the proposed numerical method accessible and adaptable for the researchers working in the field of engineering and sciences. The priori error estimate and convergence analysis are carried out to affirm the viability of the proposed method. Various examples are considered and worked out in order to illustrate its applicability and effectiveness. The results demonstrate excellent accuracy and efficiency compared to the other existing methods.
    Źródło:
    Opuscula Mathematica; 2023, 43, 4; 575-601
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A finite difference method for nonlinear parabolic-elliptic systems of second-order partial differential equations
    Autorzy:
    Malec, M.
    Sapa, L.
    Powiązania:
    https://bibliotekanauki.pl/articles/255499.pdf
    Data publikacji:
    2007
    Wydawca:
    Akademia Górniczo-Hutnicza im. Stanisława Staszica w Krakowie. Wydawnictwo AGH
    Tematy:
    partial differential equation
    parabolic-elliptic system
    finite difference method
    finite difference scheme
    consistence
    convergence
    stability
    error estimate
    uniqueness
    Opis:
    This paper deals with a finite difference method for a wide class of weakly coupled nonlinear second-order partial differential systems with initial condition and weakly coupled nonlinear implicit boundary conditions. One part of each system is of the parabolic type (degenerated parabolic equations) and the other of the elliptic type (equations with a parameter) in a cube in R1+n. A suitable finite difference scheme is constructed. It is proved that the scheme has a unique solution, and the numerical method is consistent, convergent and stable. The error estimate is given. Moreover, by the method, the differential problem has at most one classical solution. The proof is based on the Banach fixed-point theorem, the maximum principle for difference functional systems of the parabolic type and some new difference inequalities. It is a new technique of studying the mixed-type systems. Examples of physical applications and numerical experiments are presented.
    Źródło:
    Opuscula Mathematica; 2007, 27, 2; 259-289
    1232-9274
    2300-6919
    Pojawia się w:
    Opuscula Mathematica
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Local accuracy and error bounds of the improved Runge-Kutta numerical methods
    Autorzy:
    Qureshi, S.
    Memon, Z.
    Shaikh, A. A.
    Powiązania:
    https://bibliotekanauki.pl/articles/122862.pdf
    Data publikacji:
    2018
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    error estimate
    remainder term
    principal error function
    truncation error
    Lotkin bound
    granice błędu
    metoda numeryczna Runge-Kutty
    błąd obcięcia
    granica Lotkina
    funkcja błędu
    szacowanie błędu
    Opis:
    In this paper, explicit Improved Runge-Kutta (IRK) methods with two, three and four stages have been analyzed in detail to derive the error estimates inherent in them whereas their convergence, order of local accuracy, stability and arithmetic complexity have been proved in the relevant literature. Using single and multivariate Taylor series expansion for a mathematical function of one and two variables respectively, slopes involved in the IRK methods have been expanded in order to obtain the general expression for the leading or principal term in the local truncation error of the methods. In addition to this, principal error functions of the methods have also been derived using the idea of Lotkin bounds which consequently gave rise to the error estimates for the IRK methods. Later, these error estimates were compared with error estimates of the two, three, and four-stage standard explicit Runge-Kutta (RK) methods to show the better performance of the IRK methods in terms of the error bounds on the constant step-size h used for solving the initial value problems in ordinary differential equations. Finally, a couple of initial value problems have been tested to determine the maximum absolute global errors, absolute errors at the final nodal point of the integration interval and the CPU times (seconds) for all the methods under consideration to get a better idea of how the methods behave in a particular situation especially when it comes to analyzing the error terms.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 4; 73-84
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical Analysis and Simulations of Quasistatic Frictionless Contact Problems
    Autorzy:
    Fernandez Garcia, J. R.
    Han, W.
    Shillor, M.
    Sofonea, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/908327.pdf
    Data publikacji:
    2001
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    analiza numeryczna
    quasistatyka
    metoda elementów skończonych
    quasistatic contact
    Signorini condition
    normal compliance
    viscoplasticity
    variational inequalitie
    error estimate
    finite element method (FEM)
    numerical approximation
    Opis:
    A summary of recent results concerning the modelling as well as the variational and numerical analysis of frictionless contact problems for viscoplastic materials are presented. The contact is modelled with the Signorini or normal compliance conditions. Error estimates for the fully discrete numerical scheme are described, and numerical simulations based on these schemes are reported.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2001, 11, 1; 205-222
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Third order singularly perturbed delay differential equation of reaction diffusion type with integral boundary condition
    Autorzy:
    Sekar, Elango
    Tamilselvan, Ayyadurai
    Powiązania:
    https://bibliotekanauki.pl/articles/122568.pdf
    Data publikacji:
    2019
    Wydawca:
    Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
    Tematy:
    singular perturbation problem
    finite difference scheme
    delay
    integral boundary condition
    error estimate
    schemat różnic skończonych
    opóźnienie
    oszacowanie błędu
    metoda numeryczna
    metoda równań skończonych
    Opis:
    A class of third order singularly perturbed delay differential equations of reaction diffusion type with an integral boundary condition is considered. A numerical method based on a finite difference scheme on a Shishkin mesh is presented. The method suggested is of almost first order convergent. An error estimate is derived in the discrete norm. Numerical examples are presented, which validate the theoretical estimates.
    Źródło:
    Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 99-110
    2299-9965
    Pojawia się w:
    Journal of Applied Mathematics and Computational Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    A direct and accurate adaptive semi-Lagrangian scheme for the Vlasov-Poisson equation
    Autorzy:
    Campos Pinto, M.
    Powiązania:
    https://bibliotekanauki.pl/articles/929689.pdf
    Data publikacji:
    2007
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    metoda Lagrangiana
    oszacowanie błędu
    szybkość zbieżności
    fully adaptive scheme
    semi-Lagrangian method
    Vlasov-Poisson equation
    error estimate
    convergence rates
    optimal transport of adaptive multiscale meshes
    Opis:
    This article aims at giving a simplified presentation of a new adaptive semi-Lagrangian scheme for solving the (1 + 1)- dimensional Vlasov-Poisson system, which was developed in 2005 with Michel Mehrenberger and first described in (Campos Pinto and Mehrenberger, 2007). The main steps of the analysis are also given, which yield the first error estimate for an adaptive scheme in the context of the Vlasov equation. This article focuses on a key feature of our method, which is a new algorithm to transport multiscale meshes along a smooth flow, in a way that can be said optimal in the sense that it satisfies both accuracy and complexity estimates which are likely to lead to optimal convergence rates for the whole numerical scheme. From the regularity analysis of the numerical solution and how it gets transported by the numerical flow, it is shown that the accuracy of our scheme is monitored by a prescribed tolerance parameter \epsilon which represents the local interpolation error at each time step. As a consequence, the numerical solutions are proved to converge in L\infty towards the exact ones as \epsilon and \delta t tend to zero, and in addition to the numerical tests presented in (Campos Pinto and Mehrenberger, 2007), some complexity bounds are established which are likely to prove the optimality of the meshes.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2007, 17, 3; 351-359
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    An analytical and numerical approach to a bilateral contact problem with nonmonotone friction
    Autorzy:
    Barboteu, M.
    Bartosz, K.
    Kalita, P.
    Powiązania:
    https://bibliotekanauki.pl/articles/330898.pdf
    Data publikacji:
    2013
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    linearly elastic material
    bilateral contact
    nonmonotone friction law
    hemivariational inequality
    finite element method
    error estimate
    nonconvex proximal bundle method
    quasi augmented Lagrangian method
    Newton method
    metoda elementów skończonych
    szacowanie błędu
    metoda Lagrangiana
    metoda Newtona
    Opis:
    We consider a mathematical model which describes the contact between a linearly elastic body and an obstacle, the so-called foundation. The process is static and the contact is bilateral, i.e., there is no loss of contact. The friction is modeled with a nonmotonone law. The purpose of this work is to provide an error estimate for the Galerkin method as well as to present and compare two numerical methods for solving the resulting nonsmooth and nonconvex frictional contact problem. The first approach is based on the nonconvex proximal bundle method, whereas the second one deals with the approximation of a nonconvex problem by a sequence of nonsmooth convex programming problems. Some numerical experiments are realized to compare the two numerical approaches.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2013, 23, 2; 263-276
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Numerical analysis of a frictional contact problem for thermo-electro-elastic materials
    Autorzy:
    Ouafik, Youssef
    Powiązania:
    https://bibliotekanauki.pl/articles/2055046.pdf
    Data publikacji:
    2020
    Wydawca:
    Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
    Tematy:
    thermo-electro-elastic material
    frictional contact
    Finite Element Method
    error
    estimate
    numerical simulations
    Opis:
    A numerical method is presented for a mathematical model which describes the frictional contact between a thermo-electro-elastic body and a conductive foundation. The contact is described by Signorini’s conditions and Tresca’s friction law including electrical and ther- mal conductivity conditions. Our aim is to present a detailed description of the numerical modelling of the problem. To this end, we introduce a discrete scheme based on the finite element method. Under some regularity assumptions imposed on the true solution, optimal order error estimates are derived for the linear element solution. This theoretical result is illustrated numerically.
    Źródło:
    Journal of Theoretical and Applied Mechanics; 2020, 58, 3; 673--683
    1429-2955
    Pojawia się w:
    Journal of Theoretical and Applied Mechanics
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
    Tytuł:
    Revisiting the optimal probability estimator from small samples for data mining
    Autorzy:
    Cestnik, Bojan
    Powiązania:
    https://bibliotekanauki.pl/articles/330350.pdf
    Data publikacji:
    2019
    Wydawca:
    Uniwersytet Zielonogórski. Oficyna Wydawnicza
    Tematy:
    probability estimation
    small sample
    minimal error
    m-estimate
    estymacja prawdopodobieństwa
    mała próbka
    błąd minimalny
    Opis:
    Estimation of probabilities from empirical data samples has drawn close attention in the scientific community and has been identified as a crucial phase in many machine learning and knowledge discovery research projects and applications. In addition to trivial and straightforward estimation with relative frequency, more elaborated probability estimation methods from small samples were proposed and applied in practice (e.g., Laplace’s rule, the m-estimate). Piegat and Landowski (2012) proposed a novel probability estimation method from small samples Eph√2 that is optimal according to the mean absolute error of the estimation result. In this paper we show that, even though the articulation of Piegat’s formula seems different, it is in fact a special case of the m-estimate, where pa = 1/2 and m = √2. In the context of an experimental framework, we present an in-depth analysis of several probability estimation methods with respect to their mean absolute errors and demonstrate their potential advantages and disadvantages. We extend the analysis from single instance samples to samples with a moderate number of instances. We define small samples for the purpose of estimating probabilities as samples containing either less than four successes or less than four failures and justify the definition by analysing probability estimation errors on various sample sizes.
    Źródło:
    International Journal of Applied Mathematics and Computer Science; 2019, 29, 4; 783-796
    1641-876X
    2083-8492
    Pojawia się w:
    International Journal of Applied Mathematics and Computer Science
    Dostawca treści:
    Biblioteka Nauki
    Artykuł
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