Splitting Error Analysis and L-Commutativity of Operators
by
Ivan Dimov
Central Laboratory for Parallel Processing, Bulgarian Academy of Sciences, Acad. G. Bonchev Bl. 25A, 1113 Sofia, Bulgaria
Coauthors: Istvan Farago (Eötvös Loránd University, Budapest), Zahari Zlatev (Danish Air Polution Laboratory)

The error arising when splitting procedures are used in mathematical models is analyzed. The analysis is based on the study of L-commutativity of the operators used in the models. We consider L-commutativity of advection and diffusion operators which appear in many real-life models, as well as atmospheric chemistry, deposition and pollutant sources operators used in modelling of large-scale air pollution transport-reaction processes.

Necessary and sufficient conditions, under which the splitting errors are vanishing, are formulated.

Two kinds of splitting procedures are studied: the splitting used in the Danish Eulerian model (DEM splitting) and the Strang splitting procedure (Strang splitting). The splitting errors that arise when these two splitting procedures are applied in air pollution models are compared and analyzed.

Date received: February 8, 2000