Numerical Integration of dynamical systems


In this course we will introduce and study numerical integrators for stiff (or multiscale) differential equations and dynamical systems with special geometric structures (symplecticity, reversibility, first integrals, etc.). These numerical methods are important for many applications ranging from the numerical simulation of chemical reactions, fluid dynamics or mechanical systems, to the study of population dynamics or planetary motion.

Dynamics of the concentration of a reactant in a chemical reaction. Simulation with stiff (right picture) and non-stiff (left picture) solvers.

Trajectory of Jupiter, Saturn, Uranus, Neptun, Pluto over 200 000 days with explicit and implicit methods (upper left and right picture) and symplectic and symmetric methods (lower left and right picture). Picture from the book E.Hairer, C. Lubich and G. Wanner, “Geometric Numerical Integration”, Second Edition, Springer, Berlin, 2006.


Prof. Assyr Abdulle


Timothée Pouchon will be present in his office, MA C2 615, on Wednesday from 14:00 to 15:00 to answer your questions.

Organization of the course

Course: Monday from 10h15 to 12h00 at MA A3 30
Exercise session : Friday from 10h15 to 12h00 at MA A1 10


Additional session for exam preparation : Friday, 08.01.2016, 14h00 in MA B2 485

Basic definitions for Runge-Kutta methods

Week Series Week Series Week Series
Series 1
Series 2
Series 3
Series 4
Series 5
Series 6
Series 7
Series 8
Series 9
Series 10
Series 11
Series 12
Series 13



A tentative outline of the course can be found here: Syllabus.


– E. Hairer and G. Wanner, « Solving Ordinary Differential Equations II », second revised edition, Springer, Berlin, 1996

– E. Hairer, C Lubich and G. Wanner, “Geometric Numerical Integration”, second edition, Springer, Berlin, 2006

– B. Leimkuhler and S. Reich, “Simulating Hamiltonian Dynamics”, Cambridge University Press, 2005.

Java animations

(Codes by G. Vilmart)

The three body problem Sun-Jupiter-Saturn
Molecular dynamics simulation: the Lennard-Jones potential