Numerical Integration with Splitting MethodsAlexander OstermannInstitut für Mathematik, Universität Innsbruck
A mini
course at Helsinki University of Technology,
27.30.04.2009
A part of
the Special Year in Numerics 20082009
of the Finnish Mathematical
Society
Splitting
methods constitute a class of (numerical) schemes for solving initial
value problems. Roughly speaking, they decompose the vector field into
several parts and integrate these parts separately. Splitting methods
are frequently used for the time discretisation of partial differential
equations. The reason for this is that the splitting procedure yields
highly competitive time stepping schemes which can dramatically reduce
the required computational effort, compared to schemes based on the
full vector field.
The first part of the minicourse will be
devoted to splitting methods for ODEs. We shall derive the (nonstiff)
order conditions via the wellknown BakerCampbellHausdorff formula.
In
the second part, emphasis will be laid on a sound convergence theory
for splitting methods applied to time dependent partial differential
equations. In particular, we will cover the following topics:
 evolution equations with unbounded operators;
 splitting methods for Schrödinger equations;
 dimension splitting for parabolic problems;
 boundary conditions;
 highorder splitting methods for analytic semigroups;
 nonlinear problems.
References can be found here.Lectures: Monday 27.4.2009 at 10:1512:00 in room U356,
 Tuesday 28.4.2009 at 10:1512:00 in room U358,
 Wednesday 29.4.2009 at 10:1512:00 in room U322,
 Thursday 30.4.2009 at 10:1512:00 in room U322.
Computer practice sessions:
 Monday 27.4.2009 at 14:1516:00 in room Y339a,
 Tuesday 28.4.2009 at 14:1516:00 in room Y339b,
 Wednesday 29.4.2009 at 14:1516:00 in room Y338c.
Contact information: Professor Timo Eirola (Timo.Eirola@tkk.fi) Assistant Kurt Baarman (Kurt.Baarman@tkk.fi)

