A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation

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• 作者：Minghua Chen ; Weihua Deng ; ^{dengwh@lzu.edu.cn" class="auth_mail}
• 关键词：Space fractional convection diffusion equation ; Numerical stability ; Crank&ndash ; Nicolson scheme ; Two-dimensional two-sided fractional PDE ; Alternating direction implicit method
• 刊名：Applied Mathematical Modelling
• 出版年：1 July 2014
• 年：2014
• 卷：38
• 期：13
• 页码：3244-3259
• 全文大小：512 K

文摘

Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this paper, we discuss the practical alternating directions implicit method to solve the two-dimensional two-sided space fractional convection diffusion equation on a finite domain. We theoretically prove and numerically verify that the presented finite difference scheme is unconditionally von Neumann stable and second order convergent in both space and time directions.