Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-04-10T14:46:02Z | |
dc.date.available | 2006-04-10T14:46:02Z | |
dc.date.issued | 1991-04 | en_US |
dc.identifier.citation | Boyd, John P. (1991/04)."Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm." Applied Numerical Mathematics 7(4): 287-296. <http://hdl.handle.net/2027.42/29397> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6TYD-45DB1RM-1/2/b1fa12957e5c5b70b07ef603251b0e1e | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/29397 | |
dc.description.abstract | Pseudospectral discretizations of differential equations are much more accurate than finite differences for the same number of grid points N. The reason is that derivatives are approximated by a weighted sum of all N values of u(xi), rather than just three as in a second-order finite difference. The price is that the N x N pseudospectral matrix is dense with N nonzero elements (rather than three) in each row.Truncating the pseudospectral sums to create a sparse discretization fails because the derivative series are alternating and very slowly convergent. However, these series are perfect candidates for sum-acceleration methods. We show that the Euler summation can be applied to a standard pseudospectral scheme to produce an algorithm which is both exponentially accurate (like any other spectral method) and yet generates sparse matrices (like a finite difference method). For illustration, we use the sinc basis with an evenly spaced grid on x [set membership, variant] [- [infinity], [infinity]]. However, the same techniques apply equally well to Chebyshev and Fourier polynomials. | en_US |
dc.format.extent | 764544 bytes | |
dc.format.extent | 3118 bytes | |
dc.format.mimetype | application/pdf | |
dc.format.mimetype | text/plain | |
dc.language.iso | en_US | |
dc.publisher | Elsevier | en_US |
dc.title | Sum-accelerated pseudospectral methods: the Euler-accelerated sinc algorithm | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Mathematics | en_US |
dc.subject.hlbtoplevel | Science | en_US |
dc.description.peerreviewed | Peer Reviewed | en_US |
dc.contributor.affiliationum | Department of Atmospheric, Oceanic and Space Science and Laboratory for Scientific Computation, University of Michigan, 2455 Hayward Avenue, Ann Arbor, MI 48109, USA | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/29397/1/0000470.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1016/0168-9274(91)90065-8 | en_US |
dc.identifier.source | Applied Numerical Mathematics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
Files in this item
Remediation of Harmful Language
The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.
Accessibility
If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.