Determining the locations and discontinuities in the derivatives of functions

Authors:
Rick Archibald;Anne Gelb;Jungho Yoon
Affiliations:
Computer Science and Mathematics, ORNL, Oak Ridge, TN 37831, USA;Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA;Department of Mathematics, Ewha W. University, Seoul 120-750, South Korea
Venue:
Applied Numerical Mathematics
Year:
2008

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Abstract

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.