Exponentially accurate Runge-free approximation of non-periodic functions from samples on an evenly spaced grid

Applied Mathematics Letters

Volumn 20, Issue 9, 2007, Pages 971-975

  Boyd, John P ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

Author keywords

Interpolation; Runge Phenomenon; Spectral method

Indexed keywords

APPROXIMATION ALGORITHMS; CONVERGENCE OF NUMERICAL METHODS; ERROR ANALYSIS; INTERPOLATION;

NON-PERIODIC FUNCTIONS; RUNGE PHENOMENON; SPECTRAL METHOD;

FUNCTION EVALUATION;

EID: 34250701644     PISSN: 08939659     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.aml.2006.10.001     Document Type: Article

References (7)

1. Boyd J.P. Chebyshev and Fourier Spectral Methods. 2nd ed. (2001), Dover, Mineola, New York 665 pp
2. Gottlieb D., and Gottlieb S. Spectral methods for compressible reactive flows. C. R. Mec. 333 1 (2005) 3-16
3. Boyd J.P. Defeating Gibbs phenomenon in Fourier and Chebyshev spectral methods for solving differential equations. In: Jerri A. (Ed). Gibbs Phenomenon (2007), Sampling Publishing, Potsdam, New York
4. Boyd J.P. Trouble with Gegenbauer reconstruction for defeating Gibbs' phenomenon: Runge phenomenon in the diagonal limit of Gegenbauer polynomial approximations. J. Comput. Phys. 204 (2005) 253-264
5. J.P. Boyd, The Erfc-Log filter and the asymptotics of the Vandeven and Euler sequence accelerations, in: Proceedings of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 1996, pp. 267-276
6. Vandeven H. Family of spectral filters for discontinuous problems. J. Sci. Comput. 6 (1991) 159-192
7. Boyd J.P. The envelope of the error for Chebyshev & Fourier interpolation. J. Sci. Comput. 5 (1990) 311-363