This repository contains material accompanying the seminar talk by Daniel Richter and Leonard Storcks on "Classical Numerical Approaches for Solving (Stiff) Differential Equations" held in the Scientific Machine Learning Seminar by Dr. Tobias Buck from the AstroAI-Lab at Heidelberg University.
We hope, this repository can help everyone, keen on learning more on numerical solvers, stiff differential equations and programming and visualizing in Julia (although I have learned a bit of Julia only in the course of this project).
- in the current version of the slides we very strongly advocate for symplectic methods for all kinds of situations where conservational properties are of interest, which is also the "classical" standpoint; if you look, however, at a package for N-Body-Simulations like rebound, the default integrator is indeed not symplectic (see Rein et Spiegel, 2015 for reasoning on this) and for some high-precision settings something like Clean Numerical Simulations (CNS) might make sense
- Presentation slides: slides.pdf
- Efficiently solving stiff differential equations at the hand of a simplified Brussletor problem: efficiently_solfving_stiff_differential_equations.ipynb / pdf
- Analysis of a simple linear stiff system: simple_stiff_example.py
- Phase space visualization for different integrators: stream_plots.py
- Example on the stability of the explicit Euler method: euler_live.ipynb
- Figures generated by the various scripts can be found in the figures folder
We thank the whole course for the attentive listening during the seminar talk - here are the promised qustioner badges:
