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

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