Trigonometric Splines for Oscillator Simulation

TL;DR

This paper demonstrates that using trigonometric splines in oscillator simulations effectively eliminates numerical damping, preserving energy and improving reliability in autonomous system modeling.

Contribution

It introduces trigonometric splines as a solution to numerical damping issues in oscillator simulation, enhancing accuracy for spline-based adaptive methods.

Findings

Numerical damping causes artificial energy loss in oscillator simulations.

Trigonometric splines eliminate the negative effects of numerical damping.

Improved reliability in the simulation of autonomous oscillatory systems.

Abstract

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.