Temat: szacowanie błędu - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Discretization of singular systems and error estimation
Autorzy:: Karampetakis, N. P.
Karamichalis, R.
Powiązania:: https://bibliotekanauki.pl/articles/330393.pdf
Data publikacji:: 2014
Wydawca:: Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:: descriptor system
discretization
truncation error
first order hold
zero order hold
układ deskrypcyjny
dyskretyzacja
błąd obcięcia
szacowanie błędu
Opis:: This paper proposes a discretization technique for a descriptor differential system. The methodology used is both triangular first order hold discretization and zero order hold for the input function. Upper bounds for the error between the continuous and the discrete time solution are produced for both discretization methods and are shown to be better than any other existing method in the literature.
Źródło:: International Journal of Applied Mathematics and Computer Science; 2014, 24, 1; 65-73
1641-876X
2083-8492
Pojawia się w:: International Journal of Applied Mathematics and Computer Science
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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