Article ID Journal Published Year Pages File Type
4625870 Applied Mathematics and Computation 2016 25 Pages PDF
Abstract

In this paper, several difference schemes are proposed for both one-dimensional and two-dimensional space and time fractional Bloch–Torrey equations. The spatial second-order scheme and the spatial fourth-order compact scheme are established, respectively. The obtained schemes can achieve the global second-order numerical accuracy in time. The unique solvability, unconditional stability and convergence of the proposed schemes are proved by the energy method. Two ADI schemes are also discussed for the two dimensional problem. Numerical examples are given to verify the numerical accuracy and efficiency of the difference schemes.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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