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 problem in computer simulation, viz., scattering of waves from a sinusoidal boundary. The numerical method used is based on boundary collocation. This leads to highly ill-conditioned linear systems of equations, such that ensuing results may lose significant digits. The packages under consideration, each of which is based on a specific computer arithmetic, are the following: CADNA, PROFIL, MAPLE and MATLAB. We find that both CADNA and PROFIL (using stochastic and interval arithmetic, respectively) provide an effortless validation of the numerical results obtained in computer simulation, whereby we get a reliable account of the limitations of the numerical methods. (C) 1999 IMACS/Elsevier Science B.V. Ail rights reserved.
boundary collocation cadna profil interval arithmetic stochastic arithmetic grating rayleigh ansatz