On a high order numerical method for functions with singularities
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- by Knut S. Eckhoff PDF
- Math. Comp. 67 (1998), 1063-1087 Request permission
Abstract:
By splitting a given singular function into a relatively smooth part and a specially structured singular part, it is shown how the traditional Fourier method can be modified to give numerical methods of high order for calculating derivatives and integrals. Singular functions with various types of singularities of importance in applications are considered. Relations between the discrete and the continuous Fourier series for the singular functions are established. Of particular interest are piecewise smooth functions, for which various important applications are indicated, and for which numerous numerical results are presented.References
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Additional Information
- Knut S. Eckhoff
- Affiliation: Department of Mathematics, University of Bergen, Johannes Bruns gate 12, N-5008 Bergen Norway
- Email: reske@mi.uib.no
- Received by editor(s): December 11, 1996
- Received by editor(s) in revised form: March 26, 1997
- Additional Notes: This paper is partly based on work done while the author was engaged at the SINTEF Multiphase Flow Laboratory, Trondheim, Norway. The paper is also partly based on work done while the author was in residence at the Division of Applied Mathematics, Brown University, Providence, R.I., U.S.A. supported by AFOSR grant 95-1-0074 and NSF grant DMS-9500814.
- © Copyright 1998 American Mathematical Society
- Journal: Math. Comp. 67 (1998), 1063-1087
- MSC (1991): Primary 65M70, 65N35
- DOI: https://doi.org/10.1090/S0025-5718-98-00949-1
- MathSciNet review: 1459387