Fast And Efficient Finite Difference/Finite Element Method For A Class Of Time-space Fractional Bloch-Torrey Equations

In this paper,a fast and efficient finite difference/finite element method is proposed to solve the multi-term space-time fractional Bloch-Torrey equation in two dimensional domain.At present,the existing works mainly study the numerical methods of decoupled fractional Bloch-Torrey equations.In contrast,we establish the fast and low-memory numerical scheme,and discuss the relative stability and error estimation.Specifically:first,in order to fast estimation to Caputo fractional derivative and reduce the storage of numerical scheme,the sum of some exponential functions is used to approximate the kernel^-,?(0,1).Second,considering that the exact solution of the considered problem has low regularity near=0,we choose the non-uniform temporal mesh.Third,the stability and convergence are discussed for the developed semi-discrete scheme,and the error estimate is investigated for the devised fully discrete scheme in detail.Finally,some numerical tests are given to verify the correctness of the obtained theoretical results and the effectiveness of our method.