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A new characteristic finite difference method for solving the two-sided space-fractional convection–diffusion equations is presented, by combining characteristic methods and fractional finite difference methods. Stability, consistency and (therefore) convergence of the new method are discussed in this paper. An error estimate is given. Numerical experiments of this method are carried out and compared...
Fractional order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this Letter, in order to solve the two-sided fractional advection–diffusion equation, the fractional Crank–Nicholson method (FCN) is given, which is based on shifted Grünwald–Letnikov formula. It is shown that this method is unconditionally stable, consistent...
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