The use of interlacing nets for the application of relaxation methods to problems involving two dependent variables

Abstract

In the solution, by relaxation methods, of partial differential equations involving more than one dependent variable, it has been customary to find the values of all such variables at the nodes ofone net.By considering the relative accuracy of the finite difference approximations to the individual terms of the equations, and for other reasons, it is suggested that values of some of the variables be determined at the centres of the meshes, which amounts to using two interlacing nets. This idea is developed, and the method is applied to a variety of problems.