Дифузионо-таласна једначина разломљеног реда са концентрисаним капацитетом и њена апроксимација методом коначних разлика
Fractional diffusion-wave equation with concentrated capacity and its finite difference approximation
Докторанд
Delić, Aleksandra M.Ментор
Jovanović, BoškoЧланови комисије
Milovanović, GradimirDražić, Milan
Метаподаци
Приказ свих података о дисертацијиСажетак
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...
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.