(ρC ΦC)t+Δt/2=\(\frac{1}{2}\)(ρC ΦC)t+\(\frac{1}{2}\)(ρC ΦC)t+Δt.

Explanation: The Crank-Nicolson scheme uses the cell centres of both the cells which share the face which is considered. The face considered here is t-\(\frac{\Delta t}{2}\) . It is shared by the faces t and t-Δ t. So, the scheme uses both of these values for the approximation.

Explanation: The Crank-Nicolson scheme is an explicit scheme which uses the values before the face and after the face to find the value at the face. Therefore, its stability is constrained by the CFL or Courant number.

Explanation: The finite volume approach using the Crank-Nicolson scheme can be reformulated using the first-order implicit Euler scheme and then the explicit Euler scheme which is modified and used in the form of extrapolation.

Explanation: By expanding the results of the Crank-Nicolson scheme using the Taylor series expansion, the scheme is proved to be a second-ordered scheme. The third-ordered term omitted here is a dispersive term causing instabilities.