Title: Global Error Estimates and Adaptive Algorithms for Evolution ODEs Speaker: Jeff Sandelin, Colorado State University Date/Time: September 23, 2009 at 9:30 – 10:30am Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: Adaptive error control is used routinely for solving ODEs that arise in practice in science and engineering. However, traditional error control methods are generally based on some form of "local error control" that either ignores or grossly over-estimates the effects of stability, e.g. accumulation, propagation, and cancellation of error. One reason is that general classic a priori error bounds result in expressions that grow exponentially with time. On the other hand, the use of accurate a posteriori error estimates for adaptive error control is problematic because there is no clear mechanism for choosing local steps so as to minimize an error estimate in which there is significant cancellation. We discuss a new "mesoscale" approach to adaptive error control that is based on grouping time steps according to cancellation and accumulation of local step contributions so as to maintain the positive effects of cancellation. We discuss the relation to existing approaches to time step control and also describe a related approach based on "probabilistic" basis for adaptive time step control. We also discuss the implementation of the new approach in the ODE code called GAASP.CSRI POC: James R. Stewart, (505) 844-8630 |