Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-09-11T15:31:36Z | |
dc.date.available | 2006-09-11T15:31:36Z | |
dc.date.issued | 1988-06 | en_US |
dc.identifier.citation | Boyd, John P.; (1988). "Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval." Journal of Scientific Computing 3(2): 109-120. <http://hdl.handle.net/2027.42/44982> | en_US |
dc.identifier.issn | 0885-7474 | en_US |
dc.identifier.issn | 1573-7691 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/44982 | |
dc.description.abstract | “Domain truncation” is the simple strategy of solving problems on yε [-∞, ∞] by using a large but finite computational interval, [ − L, L ] Since u(y) is not a periodic function, spectral methods have usually employed a basis of Chebyshev polynomials, T n (y/L). In this note, we show that because u(±L) must be very, very small if domain truncation is to succeed, it is always more efficient to apply a Fourier expansion instead. Roughly speaking, it requires about 100 Chebyshev polynomials to achieve the same accuracy as 64 Fourier terms. The Fourier expansion of a rapidly decaying but nonperiodic function on a large interval is also a dramatic illustration of the care that is necessary in applying asymptotic coefficient analysis. The behavior of the Fourier coefficients in the limit n →∞ for fixed interval L is never relevant or significant in this application. | en_US |
dc.format.extent | 566337 bytes | |
dc.format.extent | 3115 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Kluwer Academic Publishers-Plenum Publishers; Plenum Publishing Corporation ; Springer Science+Business Media | en_US |
dc.subject.other | Appl.Mathematics/Computational Methods of Engineering | en_US |
dc.subject.other | Fourier Series | en_US |
dc.subject.other | Algorithms | en_US |
dc.subject.other | Mathematics | en_US |
dc.subject.other | Computational Mathematics and Numerical Analysis | en_US |
dc.subject.other | Mathematical and Computational Physics | en_US |
dc.subject.other | Spectral Methods | en_US |
dc.subject.other | Chebyshev Polynomials | en_US |
dc.title | Chebyshev domain truncation is inferior to fourier domain truncation for solving problems on an infinite interval | en_US |
dc.type | Article | en_US |
dc.subject.hlbsecondlevel | Science (General) | en_US |
dc.subject.hlbsecondlevel | Education | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.subject.hlbtoplevel | Social Sciences | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Atmospheric and Oceanic Science and Laboratory for Scientific Computation, University of Michigan, 2455 Hayward Avenue, 48109, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/44982/1/10915_2005_Article_BF01061252.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01061252 | en_US |
dc.identifier.source | Journal of Scientific Computing | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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