Determining the locations and discontinuities in the derivatives of functions

Rick Archibald, Anne Gelb, Jungho Yoon

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33 Scopus citations


We introduce a method for detecting discontinuities in piecewise smooth functions and in their derivatives. The method is constructed from a local stencil of grid point values and is based on a polynomial annihilation technique. By varying the order of the method and the arrangement of the corresponding stencils, the jump discontinuities of a function and its derivatives can be identified with high order accuracy. The method is efficient and robust and can be applied to non-uniform distributions in one dimension.

Original languageEnglish
Pages (from-to)577-592
Number of pages16
JournalApplied Numerical Mathematics
Issue number5
StatePublished - May 2008

Bibliographical note

Funding Information:
Anne Gelb has been supported in part by NSF grants CNS 0324957, DMS 0510813, DMS 0608844, and NIH No. EB 025533-01. Jungho Yoon has been supported by the grant Seoul Research and Business Development Program 10646.

Funding Information:
Rick Archibald has been supported by the Householder Fellowship in Scientific Computing sponsored by the DOE Applied Mathematical Sciences program. Program of Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the US Department of Energy under Contract No. DE-AC05-00OR22725. Oak Ridge National Lab, PO Box 2008, MS6367, Oak Ridge, TN 37831-6367.


  • Derivative discontinuities
  • Edge detection
  • Piecewise smooth functions
  • Polynomial annihilation


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