On the numerical solution of space–time fractional diffusion models

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• 作者：Emmanuel Hanert ; ^a ; ^{emmanuel.hanert@uclouvain.be"" rel=""nofollow}
• 关键词：Fractional derivatives ; Space– ; time fractional diffusion equation ; Pseudo-spectral method ; Mittag– ; Leffler functions
• 刊名：Computers and Fluids
• 出版年：2011
• 出版时间：July 2011
• 年：2011
• 卷：46
• 期：1
• 页码：33-39
• 全文大小：892 K

文摘

A flexible numerical scheme for the discretization of the space–time fractional diffusion equation is presented. The model solution is discretized in time with a pseudo-spectral expansion of Mittag–Leffler functions. For the space discretization, the proposed scheme can accommodate either low-order finite-difference and finite-element discretizations or high-order pseudo-spectral discretizations. A number of examples of numerical solutions of the space–time fractional diffusion equation are presented with various combinations of the time and space derivatives. The proposed numerical scheme is shown to be both efficient and flexible.