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W. Auzinger:
"Splitting methods for evolution equations, local error estimation, and adaptivity";
Keynote Lecture: ISMC 2015 - International V. Skorobohatko Mathematical Conference, Drohobych, Ukraine (invited); 2015-08-25 - 2015-08-28.

For evolution equations (ODEs or PDEs) where the right-hand side
splits up into two parts,splitting into subproblems often leads to a very
efficient approximation algorithm. The simplest cases are the first-order Lie-Trotter scheme.
Composition of the Lie-Trotter scheme with its adjoint gives
the well known second-oder Strang-Marchuk scheme, and a large variety
of higher-order multi-composition schemes have been devised in the
literature.

In this talk we address the question of finding coefficients for efficient
and accurate higher-order schemes, and the construction of local error
estimators for the purpose of adaptive step size control. Numerical results
are presented for Schrödinger equations and nonlinear wave equations.
The case of splitting into three operators is also considered.

Project Head Othmar Koch:
Adaptives Splitting für nichtlineare Schrödingergleichungen