An O(N logN) alternating-direction finite difference method for two-dimensional fractional diffusion equations |
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Authors: | Hong Wang Kaixin Wang |
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Institution: | 1. School of Mathematics, Shandong University, Jinan, Shandong 250100, China;2. Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA |
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Abstract: | Fractional diffusion equations model phenomena exhibiting anomalous diffusion that cannot be modeled accurately by the second-order diffusion equations. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional diffusion equations often generate dense or even full coefficient matrices. Consequently, the numerical solution of these methods often require computational work of O(N3) per time step and memory of O(N2) for where N is the number of grid points. |
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Keywords: | Alternating-direction method Anomalous diffusion Circulant matrix Fast Fourier transform Fractional diffusion equation Toeplitz matrix |
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