Workshop on Preservation of Stability Under Discretization

Colorado State University, Fort Collins CO

Investigators

Abstract

Stability is a term used to describe a wide variety of issues revolving around the physical observability of a solution of a differential equation. Stability lies at the very heart of the ability to make predictions about physical situations from mathematics and are particularly relevant when numerical approximation is involved, since discretization causes perturbation of both the model and the data. Numerical stability issues are typically complex because addressing such questions often requires a wide range of mathematical techniques, involving not only standard methods of numerical analysis, but ideas from dynamical systems, geometry, functional analysis, and the theory of differential equations. This raises barriers both to young researchers trying to learn about numerical stability and to communication between researchers working in different areas yet facing similar stability problems. The goal of the Workshop on the Preservation of Stability under Discretization is twofold: (1) to increase the accessibility of numerical stability issues for young researchers and (2) provide an opportunity for the exchange of information and ideas between specialists in different application areas. The Workshop will host a series of lectures by leading experts, each of whom will each address a separate aspect of stability under discretization. The lectures will be aimed towards an audience of advanced graduate students and non-specialists and will be collected into a permanent archive. In addition, the invited speakers will host a series of discussion and analysis sessions for students and young researchers. Stability is the term used to describe the situation in which a physical quantity is affected by small disturbances taking place at remote distances and times. The "butterfly" effect in chaos is one well-known stability issue, but stability issues arise in nearly every kind of physical situation from the flow of fluids and gases to computing rocket trajectories to other planets. Stability is particular relevant to numerical modeling of physical situations on computers because the modeling itself induces widespread error/disturbances. Accounting for the effects of these discretization errors is difficult because it typically requires mathematical ideas from many areas, raising barriers both to learning about how deal with stability and to communication between different areas of specialization. The goal of the Workshop on the Preservation of Stability under Discretization is twofold: (1) to increase the accessibility of numerical stability issues for young researchers and (2) provide an opportunity for the exchange of information and ideas between specialists in different application areas. The Workshop will host a series of lectures by leading experts, each of whom will each address a separate aspect of stability under discretization. The lectures will be aimed towards an audience of advanced graduate students and non-specialists and will be collected into a permanent archive. In addition, the invited speakers will host a series of discussion and analysis sessions for students and young researchers.