Journal of Scientific Computing

, Volume 71, Issue 3, pp 1212–1237 | Cite as

A New Family of Regularized Kernels for the Harmonic Oscillator

  • Benjamin W. Ong
  • Andrew J. Christlieb
  • Bryan D. Quaife


In this paper, a new two-parameter family of regularized kernels is introduced, suitable for applying high-order time stepping to N-body systems. These high-order kernels are derived by truncating a Taylor expansion of the non-regularized kernel about \((r^2+\epsilon ^2)\), generating a sequence of increasingly more accurate kernels. This paper proves the validity of this two-parameter family of regularized kernels, constructs error estimates, and illustrates the benefits of using high-order kernels through numerical experiments.


Kernel regularization Singular integrals N-body systems High-order time stepping 

Mathematics Subject Classification

65B99 65P10 70-08 70F10 70H05 



The authors would like to thank Robert Krasny, Keith Cartwright, John Verboncoeur, John Luginsland, Matthew Bettencourt, and Andrew Greenwood for their insightful discussions regarding this work, as well as anonymous referees who have made valuable suggestions to improve the presentation of this manuscript.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Benjamin W. Ong
    • 1
  • Andrew J. Christlieb
    • 2
  • Bryan D. Quaife
    • 3
  1. 1.Mathematical SciencesMichigan Technological UniversityHoughtonUSA
  2. 2.Department of MathematicsMichigan State UniversityEast LansingUSA
  3. 3.Department of Scientific ComputingFlorida State UniversityTallahasseeUSA

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