Spectral difference methods for solving differential equations

A family of recently developed techniques is explored for achieving both ma trix sparsity and rapid convergence when numerically solving differential a nd eigenvalue equations without domain decomposition. These methods, which we call spectral differences, include Boyd's sum acceleration techniques an d the Lagrange distributed approximating functional (LDAF) approach. A form ula is developed for estimating the unknown Gaussian parameter within LDAF. We implement these methods to calculate the Morse vibrational energies for diatomic iodine. For equivalent bandwidths the sum acceleration with finit e difference weights generates energies which are between two and three ord ers of magnitude more accurate than those from LDAF. (C) 1999 Elsevier Scie nce B.V. All rights reserved.