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Chebyshev rational spectral and pseudospectral methods on a semi‐infinite interval
Author(s) -
Guo Benyu,
Shen Jie,
Wang Zhongqing
Publication year - 2001
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.392
Subject(s) - chebyshev filter , chebyshev pseudospectral method , chebyshev polynomials , mathematics , chebyshev iteration , chebyshev equation , chebyshev nodes , elliptic rational functions , rational function , gauss pseudospectral method , approximation theory , interval (graph theory) , pseudospectral optimal control , pseudo spectral method , mathematical analysis , orthogonal polynomials , fourier transform , classical orthogonal polynomials , fourier analysis , elliptic curve , combinatorics , quarter period
A weighted orthogonal system on the half‐line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev rational spectral and pseudospectral methods are established; preliminary numerical results agree well with the theoretical estimates and demonstrate the effectiveness of this approach. Copyright © 2001 John Wiley & Sons, Ltd.