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.