|
| |
|
| |
|
|
Quadrature and cubature formulae with high oscillation
Gregor, Luděk ; Kofroň, Josef (advisor) ; Najzar, Karel (referee)
In the present work we study aproximation methods for values of integrals with strongly oscillating integrand. It's typical that the integrand can be split into two factors such that one is a rapidly oscillating function and the other is a smooth function - typical examples are Fourier series and Fourier integral. A usual way is aproximation of a smooth function to get product, which is simply integrable. A common choice is to aproximate smooth function instead of the whole integrand by aid of polynomials. It is possible to apply Möbius inversion technique which is applied to the Poisson summation formula. We describe methods which use orthogonal polynoms. For computing of bivariate integrals with a nondegenerate stationary point we produce an asymptotic expansion.
|
|
|
Peano kernel of the quadrature formula
Valešová, Petra ; Kofroň, Josef (advisor) ; Zítko, Jan (referee)
Nazev prace: Poanovo jadro kvadraturni formula Autor: Pctra Valcsova Katedra (ustav): Katedra numcricke matciriatiky Vcdouci bakalarskc pracc: Doc. RNDr. Josef Kofroii, CSc. c-inail vcdouciho: Josef.Kohxm^.tinff.cuni.cz Abstrakt: V pfedlozcnc praci studujcme vyjadfcni chyb kvadraturnich for- rnuli pomoci Peanova jadra. Nejprve je definovano Peanovo jadro kvadra- turni fornmlc. dale jsou uvcdcny a dokazany ricktcrc jcho vlastnosti a na dvou pfikladoch jc ukazan vypocct Peanovych jadcr. Kaslcdneje vyuzito Peanova jadra k nalezeni optimalni kvadraturni for mule. Potc jc popsana kon.strukce Rombergovy kvadraturni formulc a pfislusncho Peanova jadra. Jc uvcdcno a dokazano nekolik vlastnosti Peanovych jadcr Rombergova kvadraturniho vzorce. Dale jc na nekolika pfikladcch srovnan odhad chyby kvadraturnich formuli. Na /,;iver jc definovano Sardovo jadro kubatumi for mule a na pfi- kladc je ukazan vypocet Saixlova jadra. Klicova slova: kvadraturni vzorcc, Pcanovo jadro, chyba kvadraturni fonnule Title: Pcario kernel of the quadrature formula Author: Pctra Valesova Department: Department of Numerical Mathematics Supervisor: Doc. RNDr. Josef Kofroil, CSc. Supervisor's e-mail address: .loscf.Kofrori'il'mff.cuni.r/, Abstract: In the present work we study the expressing of errors of a qua- drature formula by Pcano kernel....
|
|
|
Overtaking model on a circular road
Krejčiřík, Radek ; Janovský, Vladimír (advisor) ; Kofroň, Josef (referee)
In this work we consider an extended follow-the-leader traffic model which was presented in [9]. The Model simulates movements of N identical cars on a circular road. There are two new aspects in this model included: velocity of each car depends on a variable reaction time and on an aggressiveness of the driver as well. Aggressiveness has a stabilizing effect on the traffic flow and variable reaction time changes the periodic dynamics in the model, but there are still some un-physical solutions. The benefit of this work is in an application of an overtaking-algorithm to the extended model. We also show an equivalent formulation of the problem as a system of ordinary differential equations with a discontinuous right-hand side. We show an existence of periodic solutions with overtaking.
|
|
| |
|
| |
|
| |
|
| |
|
| |
guest ::
RSS feed.