o:12220 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 : doctoral dissertation sr 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. Математика - Нумеричка математика / Mathematics - Numerical Mathematics Datum odbrane: 18.03.2016. null no 48115727 91552101 3521 91552100 48115727 2016-08-04T12:01:12.053Z 45 no 46 mentor Aleksandra M., 1982- Delić 2016 63 mentor Boško, 1946- Jovanović 2016 63 član komisije Gradimir, 1948- Milovanović 2016 63 član komisije Milan, 1957- Dražić 2016 109 листова 1356877 http://phaidrabg.bg.ac.rs/o:12220 no yes 7 2016-08-04T12:01:12.320Z 70 11 1066609 1066642 изводи разломљеног реда, субдифузија, супердифузија, проблем с интерфејсом, простори Собољева, слаба решења, априорна оцена, коначне резлике, брзина конвергенције fractional derivatives, subdiusion, superdiusion, interface problems,Sobolev spaces, weak solutions, a priori estimate, nite dierence, rate of convergance [517.962.8:519.63]:517.958(043.3) 1738 11A31 2016