High order accurate time integration methods
Doctoral school course, Ecole doctorale n°39, Université de Bordeaux, 2021
Notebooks of the course and instructions Course Page on ADUM website
Goal
The course aims to make the student aware of the cutting-edge algorithms used to numerically perform time integration and their properties in order to optimally choose the proper time integrator according to the considered phyisical model.
Programme
- Theory of ODEs: examples, classification, existence and uniqueness of solutions.
- Simple methods: explicit and implicit Euler, convergence, stability analysis, properties.
- High order classical methods.
- Runge–Kutta methods: construction, explicit, implicit, IMEX, error and stability analysis, properties, the Butcher tableau.
- Multistep methods: explicit, implicit methods, error and stability analysis, convergence.
- Iterative explicit high order methods: Deferred Correction (DeC), Arbitrary Derivative (ADER) methods, properties, stability and convergence analysis.
- Unconditionally positivity preserving schemes: implicit Euler, high order schemes, modified Patankar schemes and their stability and convergence analysis.
- Entropy conservative high order schemes: relaxation Runge–Kutta methods.
Prerequisites
- Basics of numerical analysis
- More details on the installation for running the notebooks can be found on the repository github.com/accdavlo/HighOrderODESolvers
Schedule
- Session 1: 14/04/2021 9:00-12:00
- Session 2: 14/04/2021 13:30-16:30
- Session 3: 15/04/2021 9:00-12:00
- Session 4: 15/04/2021 13:30-16:30