1999/01/12 by Gerald D. Quinlan, Quinlan, Gerald D.
Physics and Astronomy · #Astrophysics (astro-ph) #Computational Physics (physics.comp-ph) #FOS: Physical sciences #astro-ph #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.astro-ph/9901136
20 pages, includes 8 postscript figures, uses psfig.sty
arxiv created 1999/01/12 · arxiv updated 2009/12/01
The symmetric multistep methods developed by Quinlan and Tremaine (1990) are shown to suffer from resonances and instabilities at special stepsizes when used to integrate nonlinear equations. This property of symmetric multistep methods was missed in previous studies that considered only the linear stability of the methods. The resonances and instabilities are worse for high-order methods than for low-order methods, and the number of bad stepsizes increases with the number frequencies present in the solution. Symmetric methods are still recommended for some problems, including long-term integrations of planetary orbits, but the high-order methods must be used with caution.