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

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Abstract

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.

Keywords

Space fractional convection diffusion equation
Numerical stability
Crank–Nicolson scheme
Two-dimensional two-sided fractional PDE
Alternating direction implicit method

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