Temat: error estimate - Katalog OPAC zbiorów

Skocz do pozycji: 1.

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

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Skocz do pozycji: 2.

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

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Skocz do pozycji: 3.

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

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