Optimal prediction of underresolved dynamics
		               
				by
				
		Raz Kupferman, Department of Mathematics
               Lawrence Berkeley Laboratory and UC Berkeley

                 INSCC 110, 3:30pm  Monday, May 18th, 1998


                                Abstract



There are many problems in science whose solution is described by a set
of differential equations, but where the solution of these equations
cannot be found, even numerically, because it cannot be properly
resolved. We present a method for computing the average solution of
problems which are too complicated for adequate resolution, but where
information about the statistics of the solution is available.  The
method involves computing average derivatives by interpolation based on
linear regression, and an updating of a measure constrained by the
available crude information. Two examples will be given: a linear and a
nonlinear Schrodinger equation. 


Requests for preprints and reprints to: raz@snake.lbl.gov
This source can be found at http://www.math.utah.edu/applied-math/