Temat: fractional differential equations - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Numerical Solution of Fractional Neutron Point Kinetics Model in Nuclear Reactor
Autorzy:: Nowak, T. K.
Duzinkiewicz, K.
Piotrowski, R.
Powiązania:: https://bibliotekanauki.pl/articles/229399.pdf
Data publikacji:: 2014
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional differential equation
fractional derivatives and integrals
system of equations
nuclear reactor
neutron point kinetics
Opis:: This paper presents results concerning solutions of the fractional neutron point kinetics model for a nuclear reactor. Proposed model consists of a bilinear system of fractional and ordinary differential equations. Three methods to solve the model are presented and compared. The first one entails application of discrete Grünwald-Letnikov definition of the fractional derivative in the model. Second involves building an analog scheme in the FOMCON Toolbox in MATLAB environment. Third is the method proposed by Edwards. The impact of selected parameters on the model’s response was examined. The results for typical input were discussed and compared.
Źródło:: Archives of Control Sciences; 2014, 24, 2; 129-154
1230-2384
Pojawia się w:: Archives of Control Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 2.

Tytuł:: Numerical solution of fractional variable order linear control system in state-space form
Autorzy:: Malesza, W.
Macias, M.
Powiązania:: https://bibliotekanauki.pl/articles/201996.pdf
Data publikacji:: 2017
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: variable order fractional calculus
differential equations
analog modeling
równania różniczkowe
modelowanie analogowe
rachunek różniczkowy ułamkowego rzędu
Opis:: The aim of this paper is to introduce a matrix approach for approximate solving of non-commensurate fractional variable order linear control systems in state-space form. The approach is based on switching schemes that realize variable order derivatives. The obtained numerical solution is compared with simulation and analog model results.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2017, 65, 5; 715-724
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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Skocz do pozycji: 3.

Tytuł:: The implicit numerical method for the one-dimensional anomalous subdiffusion equation with a nonlinear source term
Autorzy:: Błasik, Marek
Powiązania:: https://bibliotekanauki.pl/articles/2086846.pdf
Data publikacji:: 2021
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional derivative
fractional integral
integro-differential equations
numerical method
finite difference method
pochodna ułamkowa
całkowanie ułamkowe
równanie całkowo-różniczkowe
metoda numeryczna
metoda elementów skończonych
Opis:: In the paper, the numerical method of solving the one-dimensional subdiffusion equation with the source term is presented. In the approach used, the key role is played by transforming of the partial differential equation into an equivalent integro-differential equation. As a result of the discretization of the integro-differential equation obtained an implicit numerical scheme which is the generalized Crank-Nicolson method. The implicit numerical schemes based on the finite difference method, such as the Carnk-Nicolson method or the Laasonen method, as a rule are unconditionally stable, which is their undoubted advantage. The discretization of the integro-differential equation is performed in two stages. First, the left-sided Riemann-Liouville integrals are approximated in such a way that the integrands are linear functions between successive grid nodes with respect to the time variable. This allows us to find the discrete values of the integral kernel of the left-sided Riemann-Liouville integral and assign them to the appropriate nodes. In the second step, second order derivative with respect to the spatial variable is approximated by the difference quotient. The obtained numerical scheme is verified on three examples for which closed analytical solutions are known.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2021, 69, 6; e138240, 1--9
0239-7528
Pojawia się w:: Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:: Biblioteka Nauki

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