• Corpus ID: 13126400

Resonances and instabilities in symmetric multistep methods

  title={Resonances and instabilities in symmetric multistep methods},
  author={Gerald D. Quinlan},
  journal={arXiv: Astrophysics},
  • G. Quinlan
  • Published 12 January 1999
  • Physics
  • arXiv: Astrophysics
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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