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Exponential Integration of Large Systems of ODEs

Jitse Niesen
Department of Applied Mathematics, University of Leeds, UK


Exponential integrators are methods for the solution of ordinary differential equations which use the matrix exponential in some form. As the solution to linear equations is given by the exponential, these methods are well suited for stiff ordinary differential equations where the stiffness is concentrated in the linear part. Such equations arise when semi-discretizing semi-linear differential equations. The biggest challenge for exponential integrators is that we need to compute the exponential of a matrix. If the matrix is not small, as is the case when solving partial differential equations, then an iterative method needs to be used. Methods based on Krylov subspaces are a natural candidate. I will describe the efforts of Will Wright (La Trobe University, Melbourne) and myself to implement such a procedure and comment on our results.

Friday, October 23, 2009
11:00AM AP&M 2402