Department of Mathematics,
Arizona State University
Thursday,
October 21, 1999, 12:15 p.m. in GWC Room 604
Department of Mathematics
Improving the Pseudospectral Collocation Method for Two-point Boundary Value Problems
Abstract
We consider the polynomial pseudospectral method for the solution
of two-point boundary value problems. This method is known to
have difficulties approximating solutions with large gradients
(shocks) away from the ends of the interval. We propose to
attach denominators to the trial functions, making them linear
rational interpolants, in such a way that the maximumnorm
of the residual is minimized. To keep the computation real, pairs
of complex-conjugate poles are successively determined. For a
Galerkin variant this can be shown to decrease the energynorm.
While, at present, no analogous result can be shown for collocation,
numerical results for several difficult problems from the literature
demonstrate the effectiveness of attaching just a few poles.
This is joint work with J.-P. Berrut, Fribourg/Switzerland.
For further information please contact:
mittelmann@asu.edu