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W. Auzinger, O. Koch, M. Thalhammer:
"Defect and local error of exponential splitting schemes";
Talk: The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Orlando, Florida, USA (invited); 2012-07-01 - 2012-07-05.

Linear or nonlinear evolution equations with a right-hand side split up into two parts can often be solved in an efficient way by splitting up the problem in each integration step. We discuss an approach for analyzing the error of exponential splitting schemes. The scheme is associated with an approximate flow, which can be characterized in detail. The defect of the scheme with respect to the given problem is now a well-defined quantity. The (local) order of the scheme can be characterized by the asymptotic behavior of the defect, and local defect integration is the theoretical basis fur a posteriori error estimation. Several aspects of this approach are discussed. As an example, Schroedinger type equations are considered.

Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen