Exponential Time Differencing (ETD) Schemes for Nonlinear Reaction-Diffusion Systems

Applied and Computational Mathematics Seminar
Monday, August 27, 2012 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Department of Mathematical Sciences, University of Wisconsin-Milwaukee
We discuss various exponential time differencing (ETD) schemes designed to handle nonlinear parabolic systems. The ETD schemes use certain Pade approximations of the matrix exponential function. These ETD schemes have potential to be implemented in parallel and their performance is very robust with respect to the type of PDE. They are unconditionally stable and computationally very fast due to the technique of computing the nonlinear part explicitly. To handle the problem of irregular initial or boundary data an adaptive ETD scheme is utilized, which adds sufficient damping of spurious oscillations. We discuss algorithm development, theory and applications.