Summary: Operator splittings and their applications
Ešotvšos LorŽand University, Budapest
We give an introduction to the operator splitting theory. Defining the
basic operator splittings methods (sequential, Marchuk-Strang, symmetri-
cally weighted sequential splitting) we analyze their accuracy and computer
realizability. We investigate the condition of the "zero splitting error" for
the above splittings. and give the connection between the operator splittings
and the semigroup theory.
Since the solution of the split sub-problems requires the use of suitable
chosen numerical methods, the interaction of the splittings and the numerical
methods is a crucial question in the application. We investigate this prob-
lem and we point out that some well-known classical schemes (like Crank-
Nicolson, Marchuk, Dyakonov, Peacman-Rachford, etc.) can be interpreted
as a results of suitable chosen splittings and numerical methods. We also list
the main benefits and drawbacks of the splitting approach.
Finally, the application of the operator splitting to the air pollution mod-
elling will be presented.