Recent Developments in Numerical Methods for Nonlinear Hyperbolic Partial Differential Equations and their Applications (08w5024)


(University of British Columbia)

Stanley Osher (UCLA)

(Brown University)

(University of California, Irvine)


Nonlinear partial differential equations (PDEs) of hyperbolic type have wide and important uses in science and engineering. To name just a few examples, consider hyperbolic conservation laws in fluid dynamics; Hamilton-Jacobi equations in optimal control, geometric optics and computer vision; or Boltzmann and kinetic equations in gas dynamics and nano technology. These PDEs pose great mathematical challenges. Closed form analytic solution is unlikely in all but the most simple cases; consequently, numerical approximations are crucial in practice.

Recently, there have been many new developments in numerical methods as well as emerging new applications for nonlinear hyperbolic PDEs. The goal of the workshop that is to be held at the Banff International Research Station on August 31 - September 5, 2008 is to bring together experts as well as junior researchers who are approaching nonlinear hyperbolic PDEs from different perspectives, including numerical analysis, algorithms and applications. An intense five day workshop in the isolated but invigorating environment of the Banff International Research Station will provide wonderful opportunities for communication and further collaborations among participants, as well as transitions of new algorithms between subfields and into applications. The former will benefit participants, while the latter the huge community who make use of these important equations.

The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnologí­a (CONACYT).