Exponential integrators - characteristics and stiff order conditions

Lien vers la page Web de l'orateur Abstract: Exponential integrators are a competitive class of methods for the numerical solution of stiff differential equations. We focus in this talk on the parabolic case where the interators treat the linear part of problem exactly and the nonlinearity in an explicit way. In the first part, we illustrate important features of such integrators and put exponential integrators into an historic perspective. In the second part, we discuss order conditions by extening the well-known concept of B-series to exponential integrators. As we are mainly interested in the stiff case, Taylor series expansions have their limitations. Our approach is based on the variation-of-constants formulat. By truncating the arising exponential B-series to a certain order (which requires regularity of the considered exact solution) we are able to identify the sought-after order conditions. In particular, we show how the stiff order conditions of arbitrary order can be obtained in a simple way from a set of recursively defined trees.