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DY: Fachverband Dynamik und Statistische Physik

DY 27: Statistical Physics II

DY 27.1: Vortrag

Dienstag, 17. März 2020, 10:00–10:15, ZEU 118

Fractional Diffusion Equation - Derivation and Numerical Approach — •Philipp Roth and Igor M. Sokolov — Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489 Berlin

We consider the continuous limit of a lattice continuous time random walk (CTRW) scheme with power-law waiting-time probability density function (WTD) with position-dependent parameters leading to a variable-order time-fractional diffusion equation. Two different situations are discussed, the ones corresponding to abrupt and to continuous changes of the parameters of the WTD. In the first case we derive the matching conditions for the solutions on the border of two subdiffusive media. In the second case we provide the solution for the case of linearly changing exponent in the WTD. We moreover present a numerical method for the solution of such equations based on the Laplace representation and the Laplace inversion using the Gaver-Stehfest algorithm, and compare our analytical solution with numerical results.