Naslov (srp)

Дифузионо-таласна једначина разломљеног реда са концентрисаним капацитетом и њена апроксимација методом коначних разлика

Autor

Delić, Aleksandra M., 1982-

Doprinosi

Jovanović, Boško, 1946-
Milovanović, Gradimir, 1948-
Dražić, Milan, 1957-

Opis (srp)

Дифузионо-таласна једначина разломљеног реда по веременској променљивој добија се из класичне дифузионе или таласне једначине заменом првог, односно другог извода по временској променљивој изводом разломљеног реда...

Opis (srp)

Математика - Нумеричка математика / Mathematics - Numerical Mathematics Datum odbrane: 18.03.2016. null

Opis (eng)

The time fractional diusion-wave equation can be obtained from the classical diffusion or wave equation by replacing the rst or second order time derivative, respectively, by a fractional derivative of order 0 < 2. In particular, depending on the value of the parameter , we distinguish subdiusion (0 < < 1), normal diusion ( = 1), superdiusion (1 < < 2) and ballistic motion ( = 2). Fractional derivatives are non-local operators, which makes it dicult to construct ecient numerical method. The subject of this dissertation is the time fractional diusion-wave equation with coecient which contains a singular distribution, primarily Dirac distribution, and its approximation by nite dierences. Initial-boundary value problems of this type are usually called interface problems. Solutions of such problems have discontinuities or non-smoothness across the interface, i.e. on support of Dirac distribution, making it dicult to establish convergence of the nite dierence schemes using the classical Taylor's expansion. The existence of generalized solutions of this initial-boundary value problem has been proved. Some nite dierence schemes approximating the problem are proposed and their stability and estimates for the rate of convergence compatible with the smoothness of the solution are obtained. The theoretical results are conrmed by numerical examples.

Jezik

srpski

Datum

2016

Licenca

Ovo delo je licencirano pod uslovima licence
Creative Commons CC BY-SA 2.0 AT - Creative Commons Autorstvo - Deliti pod istim uslovima 2.0 Austria License.

http://creativecommons.org/licenses/by-sa/2.0/at/legalcode

Predmet

OSNO - Opšta sistematizacija naučnih oblasti, Numerička matematika

OSNO - Opšta sistematizacija naučnih oblasti, Numerička matematika