A review of the Verlet and Gautschi methods for the Wave Equation

Topic: Adrian Hill - Pitt Colloquium
Time: Sep 18, 2020 03:00 PM Eastern Time (US and Canada)

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Meeting ID: 933 610 9307
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Meeting ID: 933 610 9307
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Friday, September 18, 2020 - 15:30


Speaker Information
Adrian Hill
University of Bath

Abstract or Additional Information

The Verlet time-stepping method is much favoured for the solution of nonlinear wave equations, due to its efficiency and proven energy-preserving properties. Here, we investigate its properties close to the linear stability limit for the time-step, where spurious, but ultimately stable, humps can develop in the numerical solution. We consider a somewhat non-standard approach to linear stability to explain this phenomenon, and introduce a filter, motivated by related work for the unconditionally linearly-stable Gautschi method.