CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM
                  UNIVERSITY OF COLORADO AT DENVER


TITLE:   Integration of Burgers' Equation using Simple Hierarchical Bases

SPEAKER: Bradley K. Alpert
         National Institute for Standards and Technology, Boulder

DATE:    Wednesday, March 15, 1995

PLACE:   Math Conference Room - Suite 540
         UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT: 
We present a method for the integration of nonlinear partial differential
equations that develop highly localized behavior.  The method is based on
spatial representations in "multiwavelet" bases, where a threshold
determines which coefficients are retained.  The bases, originally
constructed for the sparse representation of integral operators, consist
of discontinuous elements which, nonetheless, support representations
that can be efficiently differentiated and multiplied as required for
these problems.  Our numerical experiments, on Burgers' equation with
very low diffusion, test the ability of the method to accurately track
sharp, moving fronts.

The motivation for the use of these relatively ad hoc bases is presented.
By virtue of nonoverlapping elements on each scale, they lead to simple
implementations and can be used for a variety of geometries and boundary
conditions.