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. © 2013 Versita Warsaw and Springer-Verlag Wien.
CITATION STYLE
Yu, Q., Liu, F., Turner, I., & Burrage, K. (2013). Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D. Central European Journal of Physics, 11(6), 646–665. https://doi.org/10.2478/s11534-013-0220-6
Mendeley helps you to discover research relevant for your work.