SS
12
: Geometri numerial integrationDavid Cohen, david.ohenkit.edu, http://na.math.kit.edu/ohen/
Leture. Tutorial.
Time: Tuesday
08 . 00
-09
. 30
Time: Thursday15 . 45
-17
. 15
Plae: Room1C-03 Plae: Room1C-04
Start: April
17
Start: April19
Bakground.
Numerialmethodsfor ordinary dierential equations.
Course desription.
Ordinary dierential equations often appear in the dynamial desription of systems in physis,
hemistry,biology,et. Manydierentialequationsexhibitgeometripropertiesthatarepreserved
bythedynamis. Reently,therehas beenatrendtowardstheonstrutionofgeometrinumerial
integrators. Suhmethodsareof partiular interestin thesimulationofmehanialsystems, with
thepreservationofinvariantsastheenergy,momentumorsympletiformisimportant,espeially
inlong-term simulations(Figure
1
).Figure1: The outersolar system (www.nes.fr).
Topis:
•
Numerialmethodsfor ordinary dierentialequations.•
Hamiltonianproblems.•
Struture-preserving numerialintegrators.•
Highly osillatorydierentialequations.Target Audiene.
Masterstudents, advanedDiplomastudents,members of theResearh TrainingGroup. Students
from physis and other sienes with a basi knowledge in ordinary dierential equations are
welome.
Referenes.
E.Hairer,C.Lubih,G.Wanner: GeometriNumerialIntegration,http://www.spri ng er li nk. o m/ o nt ent /9 78 -3 -5 40 -3 06 66 -5 #s e ti on= 49 19 04 &p age =1
B. Leimkuhler, S.Reih: Simulating Hamiltonian Dynamis
E. Hairer, C. Lubih, G. Wanner: Geometri Numerial Integration Illustrated by the Störmer-
Verlet Method,
