CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



TITLE:   Optimal approximability of solutions of singularly 
         perturbed differential equations.
 

SPEAKER: Martin Stynes, Department of Mathematics, 
         University College Cork, Ireland

         
DATE:    Monday, September 15, 1997  


PLACE:   Math Conference Room 626 
         UCD Building, 1250 14th St., Denver


TIME:    noon (Refreshments served at 11:45 am) 



ABSTRACT

We consider linear singularly perturbed convection-diffusion and 
reaction-diffusion problems. While many numerical methods have been applied to 
solve such problems, little attention has been paid to the optimality (or 
otherwise) of these methods in terms of the smoothness of the solution of the 
problem and of the value of the singular perturbation parameter; small values 
of this parameter often cause a significant deterioration in the accuracy of a 
computed solution. Using the theory of $n$-widths, we clarify the best possible 
rates of convergence that can be attained in the $L_2$ norm.