On the structure of alternating direction implicit (A.D.I.) and locally one dimensional (L.O.D.) difference methods

The general structure of A.D.I. and L.O.D. difference schemes is considered with regard to their construction for time dependent problems in two and three space dimensions. By considering approximations to exp {k(L+M)} where L and M are differential operators in the space variables and k is the time step, we show how several known schemes can be viewed as having come from this type of approximation. In addition several new schemes based on this type of approximation are suggested. The arguments used are entirely informal and no attempt is made to prove the stability or convergence of the various schemes. Our aim is merely to point out a possible structure for the generation of A.D.I. and L.O.D. difference schemes. © 1972 by Academic Press Inc. (London) Limited.