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Chen, Minghua; Deng, Weihua

A second-order numerical method for two-dimensional two-sided space fractional convection diffusion equation. (English) Zbl 1427.65149

Appl. Math. Modelling 38, No. 13, 3244-3259 (2014).
Summary: 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.

Cited in 43 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
76M20 Finite difference methods applied to problems in fluid mechanics

Keywords:

space fractional convection diffusion equation; numerical stability; Crank-Nicolson scheme; two-dimensional two-sided fractional PDE; alternating direction implicit method

Software:

FODE
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Full Text: DOI arXiv

References:

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