Trigonometric Splines for Oscillator Simulation
For researchers using spline-based simulations of oscillators, this work solves a known numerical damping problem, though it is an incremental improvement.
This paper addresses numerical damping in oscillator simulation using spline methods, showing that trigonometric splines eliminate artificial energy loss, which is critical for adaptive methods.
We investigate the effects of numerical damping for oscillator simulation with spline methods. Numerical damping results in an artificial loss of energy and leads therefore to unreliable results in the simulation of autonomous systems, as e.g.\ oscillators. We show that the negative effects of numerical damping can be eliminated by the use of trigonometric splines. This will be in particular important for spline based adaptive methods.