ray-chew/symplecticity

A simple study of symplectic integrators

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.