When , the scheme is fully implicit. This scheme involves three time levels at each step of the iteration, but is explicit and is potentially much more accurate than the schemes above because of the more precise evaluation of the time derivative. Unfortunately, better truncation error is not a guarantee for the overall stability of the scheme. In the next section, the limits of applicability of these discretization schemes are analysed, in order to determine their validity and usefulness. It should be noted that three-level schemes need the knowledge of the solution at two consecutive times and to obtain the solution at .
More memory is required as well a special starting procedure.