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https://github.com/ray-chew/symplecticity

A simple study of symplectic integrators
https://github.com/ray-chew/symplecticity

euler-method numerical-integration numerical-methods symplectic-integrators

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A simple study of symplectic integrators

Host: GitHub
URL: https://github.com/ray-chew/symplecticity
Owner: ray-chew
License: apache-2.0
Created: 2018-06-28T19:24:07.000Z (over 6 years ago)
Default Branch: master
Last Pushed: 2024-03-19T15:01:34.000Z (10 months ago)
Last Synced: 2024-03-20T12:59:15.959Z (10 months ago)
Topics: euler-method, numerical-integration, numerical-methods, symplectic-integrators
Language: Jupyter Notebook
Homepage:
Size: 466 KB
Stars: 2
Watchers: 1
Forks: 0
Open Issues: 0
Metadata Files:
- Readme: README.md
- License: LICENSE

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README

# Symplecticity
A simple study of symplectic integrators.

The first-order symplectic Euler methods (Euler-A and Euler-B) and the second-order Störmer-Verlet are compared against a non-symplectic simple-Euler method for a single oscillator. The Störmer-Verlet method is then used to simulate a system of 128-coupled oscillators.

This was completed as a side project during my *numerische Mathematik* seminar at the Technische Universität Berlin.

**References**:

[1] Benedict Leimkuhler and Sebastian Reich. *Simulating Hamiltonian Dynamics*. Cambridge Monographs on Applied and Computational Mathematics. Cambridge University Press, 2005.

[2] Ernst Hairer, Christian Lubich, and Gerhard Wanner. *Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Diﬀerential Equations; 2nd ed*. Springer, Dordrecht, 2006.