THE APPLICATION OF RELAXATION METHODS TO SATISFY NORMAL-GRADIENT BOUNDARY CONDITIONS ASSOCIATED WITH THREE-DIMENSIONAL PARTIAL DIFFERENTIAL EQUATIONS

1 February 1962

journal article
Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics

Vol. 15 (1) , 43-51
https://doi.org/10.1093/qjmam/15.1.43

Abstract

The specification of a normal gradient boundary condition is of frequent occurrence in problems which require the determination of particular solutions to partial differential equations both in two and in three dimensions. Previous methods of dealing with these boundary conditions are amongst the least satisfactory techniques included in the relaxation method, even in two dimensions, and they are incapable of application in three dimensions. The present paper describes an alternative technique; it was devised in the first instance in order to tackle such conditions in three dimensions, but it is of importance also in solving problems in two dimensions. Numerical examples are given illustrating the use of the method in both cases.

Keywords

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