Comparison of four software packages applied to a scattering problem

We investigate characteristic features of four different software packages by applying them to the numerical solution of a non-trivial physical proble m in computer simulation, viz., scattering of waves from a sinusoidal bound ary. The numerical method used is based on boundary collocation. This leads to highly ill-conditioned linear systems of equations, such that ensuing r esults may lose significant digits. The packages under consideration, each of which is based on a specific computer arithmetic, are the following: CAD NA, PROFIL, MAPLE and MATLAB. We find that both CADNA and PROFIL (using stochastic and interval arithmeti c, respectively) provide an effortless validation of the numerical results obtained in computer simulation, whereby we get a reliable account of the l imitations of the numerical methods. (C) 1999 IMACS/Elsevier Science B.V. A il rights reserved.