Temat: local truncation error - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: A local truncation error estimation for a SubIval solver
Autorzy:: Sowa, M.
Powiązania:: https://bibliotekanauki.pl/articles/202058.pdf
Data publikacji:: 2018
Wydawca:: Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:: fractional calculus
numerical method
adaptive step size
local truncation error
circuit analysis
rachunek różniczkowy
metoda numeryczna
analiza obwodów
Opis:: The paper concerns an analysis for SubIval (the subinterval-based method for fractional derivative computations in initial value problems). A time step size adaptive solver is discussed, for which the formula of a local truncation error is derived. A general form for a system of linear equations is given for the considered class of problems (for which the analysis is performed in the paper). Two circuit examples are introduced to display the usefulness of the SubIval solver. For the examples that have been chosen it is possible to obtain referential solutions through completely different methods. The results obtained through the numerical solver are compared with evaluations of the referential solutions. The error estimation results obtained for the time steps of the SubIval solver are compared with the actual errors, being the differences between the numerical solutions and the referential solutions. The paper also contains a comparison of the accuracy of results obtained through the SubIval solver with the accuracies of other solvers.
Źródło:: Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 4; 475-484
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: 2.

Tytuł:: Use of partial derivatives to derive a convergent numerical scheme with its error estimates
Autorzy:: Qureshi, Sania
Adeyeye, Oluwaseun
Shaikh, Asif Ali
Powiązania:: https://bibliotekanauki.pl/articles/122734.pdf
Data publikacji:: 2019
Wydawca:: Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:: multi-derivative
local truncation error
stability
absolute relative errors
consistency
principal term
wielopochodna
pochodna cząstkowa
schemat numeryczny
błąd względny
błąd bezwzględny
Opis:: Using the idea of the partial derivative with respect to the ordinate of a given mathematical function, a new numerical scheme having third order convergence has been devised for solving initial value problems in ordinary differential equations. Such problems are deemed to be indispensable in diverse fields of science, medical and engineering and are most often required to be solved by the numerical schemes. In view of this, the proposed numerical scheme is found to be efficient in solving both autonomous and non-autonomous type of problems as supported by some numerical experiments in the present study. Using the Taylor expansion for the slopes involved in the scheme, the leading term of the local truncation error is shown to have contained Ϭ(h⁴) which proves third order accuracy of the scheme. In addition to this, consistency and linear stability analysis of the proposed scheme has extensively been discussed. Numerical experiments show better performance of the proposed numerical scheme when compared with existing numerical schemes of the same order as that of the scheme proposed. CPU time (seconds), maximum absolute relative error and the absolute relative error, computed at the last grid point of the integration interval for the associated initial value problem, are the parameters to test the performance of the proposed numerical scheme. MATLAB Version: 9.4.0.813654 (R2018a) in double-precision on a personal computer equipped with a Processor Intel (R) Core(TM) i3-4500U CPU@ 1.70 GHz running under the Windows 10 operating system has been employed in order to carry out all the required numerical computations.
Źródło:: Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 4; 73-83
2299-9965
Pojawia się w:: Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:: Biblioteka Nauki

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