Exponentially Accurate Approximations to Piece-Wise Smooth Periodic Functions

被引：24

作者：

Geer J. ^{[1
,2
]}

Banerjee N.S. ^{[1
]}

机构：

[1] Dept. of Syst. Sci. and Indust. Eng., Watson Sch. of Eng. and Appl. Sci., Binghamton University, Binghamton

[2] Inst. Comp. Applic. Sci. and Eng., NASA Langley Research Center, Hampton

来源：

Journal of Scientific Computing | 1997年 / 12卷 / 3期

基金：

美国国家航空航天局;

关键词：

Exponentially accurate approximations; Fourier series; Piecewise smooth functions;

D O I：

10.1023/A:1025649427614

中图分类号：

学科分类号：

摘要：

A family of simple, periodic basis functions with "built-in" discontinuities are introduced, and their properties are analyzed and discussed. Some of their potential usefulness is illustrated in conjunction with the Fourier series representation of functions with discontinuities. In particular, it is demonstrated how they can be used to construct a sequence of approximations which converges exponentially in the maximum norm to a piece-wise smooth function. The theory is illustrated with several examples and the results are discussed in the context of other sequences of functions which can be used to approximate discontinuous functions.

引用

页码：253 / 287

页数：34

共 12 条

[1]

Bary N.K., A Treatise on Trigonometric Series, (1964)

[2]

Geer J., Rational trigonometric approximations using Fourier series partial sums, J. Sci. Comp., 10, pp. 325-356, (1995)

[3]

Gottlieb D., Shu C., Solomonoff A., Vandeven H., On the Gibbs phenomena 1: Recovering exponential accuracy from the Fourier partial sum of a non-periodic analytic function, J. Comp. and Appl. Math., 43, pp. 81-98, (1992)

[4]

Gottlieb D., Shu C., Resolution properties of the Fourier method for discontinuous waves, Comp. Meth. Appl. Mech. Eng., 116, pp. 27-37, (1994)

[5]

Gottlieb D., Shu C., On the Gibbs phenomena III: Recovering exponential accuracy in a sub-interval from a spectral partial sum of a piecewise analytic function, SIAM J. Num. Anal., 33, pp. 280-290, (1996)

[6]

Gottlieb D., Shu C., On the Gibbs phenomena IV: Recovering exponential accuracy in a sub-interval from a Gegenbauer partial sum of a piecewise analytic function, Math. of Comp., 64, pp. 1081-1096, (1995)

[7]

Gottlieb D., Shu C., On the Gibbs phenomena V: Recovering exponential accuracy from collocation point values of a piecewise analytic function, Numerische Mathematic, (1996)

[8]

John F., Partial Differential Equations, (1982)

[9]

Kreyszig E., Advanced Engineering Mathematics (Fourth Edition), (1979)

[10]

Lanczos C., Discourse on Fourier Series, (1966)

← 1 2 →