Abstract
In this paper, an implicit finite difference scheme combined with Kansa meshless method is proposed for the two-dimensional time and space fractional Bloch-Torrey equation. The Caputo derivative with respect to time is discretized by finite difference method based on Alikhanov's super convergent approximation while Riesz derivative with respect to spatial variables by Kansa meshless method. The convergence and stability of the time semi-discretization are proven using energy method. The convergence order in time direction is proven to be 2. The implementation of the full discretization is discussed in detail. Especially, the issue of calculation of Riesz derivative of RBF is addressed. Numerical examples are given which verify the feasibility of the proposed method.
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