### Finite Difference Simulation of a One Dimensional Harmonic Oscillator

## A comparison of three finite difference techniques

This experiment concern the comparison of three
finite difference methods to the computational
simulation of a simple harmonic oscillator. The
techniques employed here were the Euler technique,
the velocity form of the Verlet algorithm, and Gear 3rd
order predictor-corrector method. The experiment
concluded that the Euler algorithm was far too
inaccurate and unstable for serious use, and also that
while the Gear method is consistently the most
accurate (once a suitable time step has been found),
the inherent stability of the Verlet system (irrespective
of time step) makes it more suitable for general use.

Particle Methods I: A comparison of three finite-difference time-integration techniques. (3rd Year)