Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , 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.
['Hong Sun', 'Zhi-zhong Sun', 'Guang-hua Gao']
I am writing a research paper on a idea Some high order difference schemes for the space and time fractional Bloch-Torrey equations
[{"from": "human", "value": "I am writing a research paper on a idea Some high order difference schemes for the space and time fractional Bloch-Torrey equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: , 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."}]