Browsing Mathematics by Author "Hodžić, Sandra"
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Hodžić, Sandra (Beograd , 2016)[more][less]
Abstract: In recent years there has been increasing interest in modeling the physical and chemical processes with equations involving fractional derivatives and integrals. One of such equations is the subdi usion equation which is obtained from the di usion equation by replacing the classical rst order time derivative by a fractional derivative of order with 0 < < 1: The subject of this dissertation is the initial-boundary value problem for the subdi usion equation and its approximation by nite di erences. At the beginning, the one-dimensional equation is observed. The existence and the uniqueness of weak solution is proved. The stability and the convergence rate estimates for implicite and the weighted scheme are obtained. The main focus is on two-dimensional subdi usion problem with Laplace operator as well as problem with general second-order partial di erential operator. It is assumed that the coe cients of the di erential operator satisfy standard ellipticity conditions that guarantees existence of solution in appropriate spaces of Sobolev type. In that case, apart from above mensoned, we constructed the additive and the factorized di erence schemes. We investigated their stability and convergence rate depending on the smoothness of the input data and of generalized solution. URI: http://hdl.handle.net/123456789/4455 Files in this item: 1
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