Mini-course on Geometric Numerical Integration
February 16-18, 2016 Fundação Getulio Vargas
Ordinary differential equations (ODEs) often
appear in the dynamical description
of systems in physics, chemistry, biology, engineering,
etc. Many differential equations exhibit
geometric properties that are preserved
by the dynamics. Recently, there has been a
trend towards the construction of
geometric numerical integrators.
Such numerical methods are of particular interest
in the simulation of mechanical systems,
where the preservation of invariants such as the energy,
momentum or symplectic form is important,
especially in long-term simulations
(of the outer solar system for example).
This mini-course offers a first introduction to the field of
Geometric Numerical Integration (GNI). In short, we will be
interested in the development and numerical analysis of
structure-preserving numerical methods for differential equations.
Topics covered in this mini-course are:
Brief exposition of classical numerical methods for ODEs
Numerical methods that preserve properties of Hamiltonian systems
Problems with highly oscillatory solutions
GNI for partial differential equations and stochastic differential equations.
These topics will be illustrated by applications from physics, molecular dynamics
The mini-course will be complemented by theoretical and practical exercises in Matlab.
Lectures (Auditório 1333): Tuesday 16.02.16, 9:20-12:00. Wednesday 17.02.16, 9:20-12:00. Thursday 18.02.16, 9:20-12:00.
Computer Labs (Laboratório 422): Wednesday 17.02.16, 14:00-17:00. Thursday 18.02.16, 14:00-17:00.
Lecture notes of the mini-course (18.02.2016).
Solutions to the assignments (18.02.2016).
Link to the lecture Introduction to PDE Constrained Optimization by Eddie Wadbro (15.02.2016)
This mini-course is organised by Hugo de la Cruz and David Cohen
within the framework Initiation Grants of the Swedish Foundation for
International Cooperation in Research and Higher Education
we gratefully acknowledge its financial support.
We thank Fundação Getulio Vargas for the hospitality.
Department of Mathematics and Mathematical Statistics
Hugo de la Cruz
Escola de Matemática Aplicada
Fundação Getulio Vargas
B-22250900 Rio de Janeiro
last modifications: 18.02.16