Instabilities and Inaccuracies in the Integration of Highly Oscillatory Problems

By means of a two-frequency test problem, we analyze the instabilities and inaccuracies that may impair the performance of multiple time steps/split operator integrators in highly oscillatory situations, such as those encountered in molecular dynamics, astrophysics, or partial differential equations...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2009-01, Vol.31 (3), p.1653-1677
Main Authors: Calvo, M. P., Sanz-Serna, J. M.
Format: Article
Language:English
Subjects:
Astrophysics
Error analysis
Impulses
Instability
Integrators
Mathematical functions
Methods
Molecular dynamics
Numerical analysis
Operators
Partial differential equations
Stability
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Summary:By means of a two-frequency test problem, we analyze the instabilities and inaccuracies that may impair the performance of multiple time steps/split operator integrators in highly oscillatory situations, such as those encountered in molecular dynamics, astrophysics, or partial differential equations describing waves. Considered are the impulse (Verlet-I/r-RESPA) method, the mollified impulse method, and the reversible averaging integrator. The analysis covers errors in positions, momenta, and energy.
ISSN:1064-8275
1095-7197
DOI:10.1137/080727658