Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D
| Autor: | Kevin Burrage, Fawang Liu, Qiang Yu, Ian Turner |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: |
Discretization
Anomalous diffusion bounded domains Operator (physics) Physics QC1-999 General Physics and Astronomy fractional bloch-torrey equation fractional centered difference Domain (mathematical analysis) Fractional calculus Matrix (mathematics) symbols.namesake Dirichlet boundary condition symbols Applied mathematics implicit numerical method Fractional quantum mechanics matrix transfer technique Mathematics |
| Zdroj: | Open Physics, Vol 11, Iss 6, Pp 646-665 (2013) |
| ISSN: | 2391-5471 |
| Popis: | Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative; Model-2 with the one-dimensional fractional Laplacian operator; and Model-3 with the two-dimensional fractional Laplacian operator.Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions. |
| Databáze: | OpenAIRE |
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