Application of the difference Gaussian rules to solution of hyperbolic problems

Two of the authors earlier suggested a method of calculating special grid s teps for three point finite-difference schemes which yielded exponential su perconvergence of the Neumann-to-Dirichlet map. We apply this approach to s olve the two-dimensional time-domain wave problem and the 2.5-D elasticity system in cylindrical coordinates. Our numerical experiments exhibit expone ntial convergence at prescribed points, with the cost per grid node close t o that of the standard second order finite-difference scheme. The scheme de monstrates high accuracy with slightly more than two grid points per wavele ngth. The reduction of the grid size by one order compared to the standard scheme with the equidistant grids is observed. (C) 2000 Academic Press.