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《Journal of Zhengzhou University(Natural Science Edition)》 2019-01
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Douglas-Gunn Finite Difference Scheme for Three-dimensional Space Fractional Advection Diffusion Equation

NIE Yufeng;HU Jiahui;WANG Jungang;Research Center for Computational Science,Northwestern Polytechnical University;College of Science,Henan University of Technology;  
Due to the non-locality of fractional derivatives,fractional partial differential equations were better to describe anomalous diffusion phenomena than other methods. However,while enjoying the convenience from mathematical modeling,it also caused lots of trouble especially in solving multidimensional cases. An efficient numerical algorithm was proposed for solving the three-dimensional space fractional advection diffusion equation(SFADE) by generalizing the Douglas-Gunn scheme. Stability and convergence of the method were proved by the matrix method. The derived alternating direction implicit(ADI)finite difference scheme had the second order accuracy in both time and space directions,respectively.The efficiency and convergence orders were finally demonstrated by some numerical examples.
【Fund】: 国家自然科学基金项目(11471262)
【CateGory Index】: O241.8
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