Exponentially Accurate Approximations to Piece-Wise Smooth Periodic Functions

Journal of Scientific Computing

Volumn 12, Issue 3, 1997, Pages 253-287

  Geer, James ^a,b   Banerjee, Nana Saheb ^a  

^a State University of New York at Binghamton   (United States)

^b NASA LANGLEY RESEARCH CENTER   (United States)

Author keywords

Exponentially accurate approximations; Fourier series; Piecewise smooth functions

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; FUNCTIONS; PIECEWISE LINEAR TECHNIQUES;

DISCONTINUOUS FUNCTIONS; PERIODIC BASIS FUNCTIONS; PIECEWISE SMOOTH FUNCTIONS;

APPROXIMATION THEORY;

EID: 0031224488     PISSN: 08857474     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1025649427614     Document Type: Article

References (12)

1. Bary, N. K. (1964). A treatise on Trigonometric Series. MacMillan. New York.
2. Geer, J. (1995). Rational trigonometric approximations using Fourier series partial sums, ICASE Rep. No. 93-68 and J. Sci. Comp. 10, 325-356.
3. Gottlieb, D., Shu, C., Solomonoff, A., and Vandeven, H. (1992). On the Gibbs phenomena 1: recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function. ICASE Rep. No. 92-4 and J. Comp. and Appl. Math. 43, 81-98.
4. Gottlieb, D., and Shu, C. (1994). Resolution properties of the Fourier method for discontinuous waves. ICASE Rep. No. 92-27 and Comp. Meth. Appl. Mech. Eng. 116, 27-37.
5. Gottlieb, D., and Shu, C. (1996a). On the Gibbs phenomena III: recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function. ICASE Rep. No. 93-82 and SIAM J. Num. Anal. 33, 280-290.
6. Gottlieb, D., and Shu, C. (1995). On the Gibbs phenomena IV: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function. ICASE Rep. No. 94-33 and Math. of Comp. 64, 1081-1096.
7. Gottlieb, D., and Shu, C. (1996b). On the Gibbs phenomena V: Recovering exponential accuracy from collocation point values of a piecewise analytic function. ICASE Rep. No. 94-61 and Numerische Mathematic (to appear).
8. John, F. (1982). Partial Differential Equations, Springer-Verlag, New York.
9. Kreyszig, E. (1979). Advanced Engineering Mathematics (fourth edition). Wiley, New York.
10. Lanczos, C. (1966). Discourse on Fourier Series, Hafner Publishing, New York.
11. Thompson, W. J. (1992). Fourier series and the Gibbs phenomena. Am. J. Phys. 60 (5). 425-429.
12. Tolstov, G. P. (1962). Fourier Series (translated from the Russian by R. A. Silverman). Prentice-Hall, New Jersey.