Comments on “The Relative Efficiency of Certain Schema in the Solution of a Poisson Equation”

Abstract

Truncation errors of four stencils for evaluating the two-dimensional Laplacian operator are discussed, and response functions are computed. The efficiencies of the stencils, in terms of number of iterations and computer time required, for solving Poisson's equation by relaxation is investigated. The dependence on the relaxation coefficient of the number of iterations required and the error of the solution is shown for a number of examples.