Finite difference approximation of space-fractional diffusion problems: The matrix transformation method

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• 作者：Bé ; la J. Szekeres ^{szbpagt@cs.elte.hu} ; Ferenc Izsá ; k ; ^{izsakf@cs.elte.hu}
• 关键词：Fractional-order diffusion ; Matrix transformation method ; Finite difference method
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：261-269
• 全文大小：419 K
• 卷排序：73

文摘

A mathematical analysis is presented to establish the convergence of the matrix transformation (or matrix transfer) method for the finite difference approximation of space-fractional diffusion problems. Combined this with an implicit Euler time discretization, the optimal order convergence is proved with respect to the discrete L2L2 and the maximum norm. The analysis is performed on general two and three-dimensional domains with homogeneous boundary conditions. The corresponding error estimates are illustrated with some numerical experiments.