Thursday,
February 10, 2005, 12:15 p.m. in GWC Room 604
Department of Mathematics&Statistics
Stability of ADI methods applied to convection-diffusion equations with
mixed-derivative terms
Abstract
In many modern application areas, such as financial option pricing and molecular biology, convection-diffusion equations arise with spatial dimensions that are greater than one. For the effective numerical solution of these equations, conventional numerical methods are in general not adequate and tailored discretization methods are required. Operator-splitting methods are particularly promising candidates for this. These methods have already been applied successfully in special cases, for example when there are no cross-derivative terms present in the equation. However, in the above mentioned application areas, general multi-dimensional convection-diffusion equations arise. The question of whether or not splitting methods can be useful in these cases is still under investigation, in particular since their stability and convergence properties are often hard to assess.
Encouraging stability results for ADI type methods have recently been obtained in joint work with Bruno Welfert (ASU). These results will be addressed in this talk.
For further information please contact:
mittelmann@asu.edu