Let us now attempt a different discretization of the original partial differential equation given by Eq. (3.3). Here we express the spatial difference on the right-hand side in terms of averages between and time level

(5.1)

The differencing shown in Eq. (5.1) is known as the Crank-Nicolson implicit scheme.

The unknown is not only expressed in terms of the known quantities at time level but also in terms of unknown quantities at time level . Hence Eq. (5.1) at a given grid point , cannot itself result in a solution of .