Title: Efficient and accurate spectral methods for linear and nonlinear wave equations


				 Jie Shen
                        Department of Mathematics
                            Purdue University
                        West Lafayette, IN  47907
                       e-mail: shen@math.purdue.edu
                Web page: http://www.math.purdue.edu/~shen


Abstract: 
In recent years, spectral methods have become increasingly popular among 
computational scientists and engineers because of their superior accuracy and 
efficiency when properly implemented. I shall present some recent developments
in spectral-Galerkin methods for the Helmholtz equation (in wave scattering), 
nonlinear Schrodinger equations and nonlinear wave equations. Applications to 
the KDV equation and Bose-Einstein condensates will be discussed.