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)