Exponentially convergent Fourier-Chebshev quadrature schemes on bounded and infinite intervals
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-09-11T15:31:32Z | |
dc.date.available | 2006-09-11T15:31:32Z | |
dc.date.issued | 1987-06 | en_US |
dc.identifier.citation | Boyd, John P.; (1987). "Exponentially convergent Fourier-Chebshev quadrature schemes on bounded and infinite intervals." Journal of Scientific Computing 2(2): 99-109. <http://hdl.handle.net/2027.42/44981> | en_US |
dc.identifier.issn | 0885-7474 | en_US |
dc.identifier.issn | 1573-7691 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/44981 | |
dc.description.abstract | The Clenshaw-Curtis method for numerical integration is extended to semi-infinite ([0, ∞] and infinite [-∞, ∞] intervals. The common framework for both these extensions and for integration on a finite interval is to (1) map the integration domain to l ε [0, π ], (2) compute a Fourier sine or cosine approximation to the transformd integrand via interpolation, and (3) integrate the approximation. The interpolation is most easily performed via the sine or cosine cardinal functions, which are discussed in the appendix. The algorithm is mathematically equivalent to expanding the integrand in (mapped or unmapped) Chebyshev polynomials as done by Clenshaw and Curtis, but the trigonometric approach simplifies the mechanics. Like Gaussian quadrature, the error for the change-of-coordinates Fourier method decreases exponentially with N , the number of grid points, but the generalized Curtis-Clenshaw algorithm is much easier to program than Gaussian quadrature because the abscissas and weights are given by simple, explicit formulas. | en_US |
dc.format.extent | 462757 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 | Rational Chebyshev Functions | en_US |
dc.subject.other | Appl.Mathematics/Computational Methods of Engineering | 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 | Quadrature | en_US |
dc.subject.other | Adaptive Quadrature | en_US |
dc.subject.other | Numerical Integration | en_US |
dc.title | Exponentially convergent Fourier-Chebshev quadrature schemes on bounded and infinite intervals | 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, University of Michigan, 48109, Ann Arbor, Michigan | en_US |
dc.contributor.affiliationumcampus | Ann Arbor | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/44981/1/10915_2005_Article_BF01061480.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1007/BF01061480 | en_US |
dc.identifier.source | Journal of Scientific Computing | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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