A note on the “nested iterations” method

The "nested iterations" method of numerical solution of elliptic partial differential equations has been suggested by Kronsj5 and Dahlquist [I]. It has also been pointed out in the paper that the idea of nested iterations had been discussed by other authors, see [2], [3], [4] and [5], for example. The main concept of the nested iterations approach is to use the results of comparatively inexpensive computations with coarse grids for the construction of an initial approximation to the difference equation for a finer grid. The accuracy of the initial approximation is then so good that it even allows the application of Richardson extrapolation to the results after a rather small number of iterations. The aim of this note is to report some computational comparisons of the results based on the initial approximations computed (a) as suggested in [1], and (b) as suggested in [3]. (Note: the papers [4] and [5] are devoted to the analysis of the con