# Resonances and instabilities in symmetric multistep methods

@article{Quinlan1999ResonancesAI, title={Resonances and instabilities in symmetric multistep methods}, author={Gerald D. Quinlan}, journal={arXiv: Astrophysics}, year={1999} }

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…

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