where, upon introducing a set of mesh points each identified by an (n + 1 )-tuple of integers K = (Ko , K1 , * * * , Kn), we choose for each non-initial point K a subset of mesh points S(K) not containing K. The scheme represented by (2) will be explicit if the mesh points can be ordered in such a way that points at which initial conditions are given are "first," and S(K) contains only predecessors of K. Frequently S(K) contains only points at an earlier time than K, but this need not be the case. Now, (1) is homogeneous in u; therefore the constant functions are solutions of (1). We require for consistency that constants also be solutions of (2), which imposes the condition