Follow this link for an illustrative example of the different dynamical properties of numerical methods.
Goal: To introduce the theory and application of numerical methods for initial value problems in ordinary and stochastic differential equations.
Meets:
Weeks 36 - 49, except week 43
(Sep. 2 - Dec. 4, 2008 except 21, 23 Oct.)
Tuesday 15:00-17:00, REC-P.015/A
Thursday 9:00-11.00, REC-P.015/B
Summary:
This course provides a thorough introduction to the numerical treatment
of continuous dynamical systems, both deterministic and stochastic. We make
the acquaintence of three classes of methods: Runge-Kutta, multistep, and
vector-field splitting methods; and analyze their approximation properties
and convergence. For integrations on intervals, we discuss important
aspects of asymptototic behavior, such as linear stability of equilibria
and preservation of invariant sets. As a unique aspect, we give special
attention to the parallels between our subject and the theories of
continuous and discrete dynamical systems. Such methods enjoy wide-spread
use in applications such as mathematical physics, biology and finance, from
which we draw examples.
Follow this link for an illustrative example of the different dynamical properties of numerical methods.
Topics:
The course will cover the following topics:
Lecturer:
Jason Frank
Centrum Wiskunde & Informatica (CWI)
Kruislaan 413, Room M259
tel: +31 20 5924096
e-mail:
Jason Frank
www: http://www.cwi.nl/~jason
Lecture Notes
The lecture notes appear here and are updated upon occasion.
Sample Matlab programs: (Directory listing)