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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

A note on a generalisation of a method of Douglas


Author: Graeme Fairweather
Journal: Math. Comp. 23 (1969), 407-409
MSC: Primary 65.68
MathSciNet review: 0243756
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Abstract: In this note, the high-order correct method of Douglas [1] for the diffusion equation in one space variable is extended to $ q \leqq 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.


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DOI: http://dx.doi.org/10.1090/S0025-5718-1969-0243756-4
PII: S 0025-5718(1969)0243756-4
Article copyright: © Copyright 1969 American Mathematical Society