A numerical treatment for the boundary value, problem involving the Helmholtz equation Deltau - lambda(2)u = f is presented. The method is a five-point formula with an improved accuracy when compared with the usual finite difference method. Besides, the accuracy evaluation is provided in analytical form and the classical difference scheme is seen as a truncated series approximation to the present method. The idea comes from approximations to analytical solutions to the Dirichlet problem inside a ball, based on the Green identity. The homogeneous and the nonhomogeneous parts are evaluated in separate expressions, and the precision error yielded is of order O(h(2)). Some numerical examples and comparisons are presented. (C) 2001 IMACS. Published by Elsevier Science B.V. All rights reserved.414459479