and Applied Analysis 3 andX E = x−uΔt (similarly we see thatX E = x−2uΔt for the two-step methods). In (7) with X being replaced by X E , we have φ n+1 − φ n (x − uΔt) Δt − νΔφ n+1 = f n+1 . (9) On the other hand, (9) can be derived by MMOC [5]. In fact, with u = (u 1 , u 2 ), let s denote the direction vector (1, u 1 , u 2 ), and define the operator d ds := 1 θ ( ∂ ∂t + u ⋅ ∇) , (10) with θ(x,...

Article history: Received 27 June 2013 Received in revised form 22 January 2014 Accepted 25 March 2014 Available online 2 April 2014

Fractional-order diffusion equations are viewed as generalizations of classical diffusion equations, treating super-diffusive flow processes. In this paper, in order to solve the fractional advection-diffusion equation, the fractional characteristic finite difference method is presented, which is based on the method of characteristics (MOC) and fractional finite difference (FD) procedures. The ...

Using classic differential quadrature formulae and uniform grids, this paper systematically constructs a variety of high-order finite difference schemes, and some of these schemes are consistent with the so-called boundary value methods. The derived difference schemes enjoy the same stability and accuracy properties with correspondent differential quadrature methods but have a simpler form of c...