MVEX01-22-02 Geometric Numerical Integration of Differential Equations

Ordinary differential equations (ODEs) arise everywhere in sciences and engineering: Newton’s law in physics, N-body problems in molecular dynamics or astronomy, populations models in biology, mechanical systems in engineering, etc. One can find analytical solutions to ODEs only in exceptional cases! It is therefore extremely important to rely on efficient numerical simulations of ODEs. 

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 long-term simulations of the outer solar system for instance. 

The goal of the bachelor thesis is to provide students with a practical and accessible introduction to geometric numerical integration (GNI) of ODEs. This will be done by reading parts of the book "Geometric Numerical Integration" to understand the theory behind GNI and by testing novel numerical schemes on applications from celestial mechanics, molecular dynamics problems, or other applications of interest to the students. 

Main reference: Hairer E, Lubich C and Wanner G (2006), "Geometric Numerical Integration", Berlin Vol. 31 Springer-Verlag.

The report will be written in Swedish.

Projektkod: MVEX01-22-02
Gruppstorlek: 3-4 studenter
Målgrupp: GU- och Chalmersstudenter. För GU-studenter räknas projektet som ett projekt i Tillämpad matematik (MMG900/MMG920).
Projektspecifika förkunskapskrav: Basic knowledge in ODE, knowledge of a scientific programming language such as matlab for example.
Se respektive kursplan för allmänna förkunskapskrav. Utöver de allmänna förkunskapskraven i MVEX01 ska Chalmersstudenter ha avklarat kurser i en- och flervariabelanalys, linjär algebra och matematisk statistik.
Handledare: David Cohen, 031-7723021, david.cohen@chalmers.se
                        Annika Lang, 031-772 5356, annika.lang@chalmers.se
Examinator: Maria Roginskaya, Ulla Dinger
Institution: Matematiska vetenskaper

Sidansvarig Publicerad: må 04 okt 2021.