Some high order difference schemes for the space and time fractional Bloch–Torrey equations

Hong Sun, Zhi-zhong Sun and Guang-hua Gao

Applied Mathematics and Computation, 2016, vol. 281, issue C, 356-380

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.

Keywords: Bloch–Torrey equation; Fractional differential equation; Riesz derivative; Finite difference scheme; Convergence; Stability (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:281:y:2016:i:c:p:356-380

DOI: 10.1016/j.amc.2016.01.044

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