A Note on a Generalisation of a Method of Douglas

1. Abstract and Introduction. In this note, the high-order correct method of Douglas [1] for the diffusion equation in one space variable is extended to q ^ 3 space variables. The resulting difference equations are then solved using the A. D. I. technique of Douglas and Gunn [3]. When q = 2, this method is equivalent to that of Mitchell and Fairweather [5] while q = 3 provides a method which is similar to Samarskiï's method [6] and of higher accuracy than that of Douglas [2]. When the proposed methods are used to solve the diffusion equation with timeindependent boundary conditions, they have the advantage that no boundary modification (see [4]) is required to maintain accuracy. |