The Rate of Convergence of Fourier Coefficients for Entire Functions of Infinite Order with Application to the Weideman-Cloot Sinh-Mapping for Pseudospectral Computations on an Infinite Interval
dc.contributor.author | Boyd, John P. | en_US |
dc.date.accessioned | 2006-04-10T18:22:55Z | |
dc.date.available | 2006-04-10T18:22:55Z | |
dc.date.issued | 1994-02 | en_US |
dc.identifier.citation | Boyd, John P. (1994/02)."The Rate of Convergence of Fourier Coefficients for Entire Functions of Infinite Order with Application to the Weideman-Cloot Sinh-Mapping for Pseudospectral Computations on an Infinite Interval." Journal of Computational Physics 110(2): 360-372. <http://hdl.handle.net/2027.42/31817> | en_US |
dc.identifier.uri | http://www.sciencedirect.com/science/article/B6WHY-45PTPT7-H/2/f106f2c19f8d52f065867019cf937399 | en_US |
dc.identifier.uri | https://hdl.handle.net/2027.42/31817 | |
dc.description.abstract | We analytically compute the asymptotic Fourier coefficients for several classes of functions to answer two questions. The numerical question is to explain the success of the Weideman-Cloot algorithm for solving differential equations on an infinite interval. Their method combines Fourier expansion with a change-of-coordinate using the hyperbolic sine function. The sinh-mapping transforms a simple function like exp(-z2) into an entire function of infinite order. This raises the second, analytical question: What is the Fourier rate of convergence for entire functions of an infinite order? The answer is: Sometimes even slower than a geometric series. In this case, the Fourier series converge only on the real axis even when the function u (z) being expanded is free of singularities except at infinity. Earlier analysis ignored stationary point contributions to the asymptotic Fourier coefficients when u(z) had singularities off the real z-axis, but we show that sometimes these stationary point terms are more important than residues at the poles of u(z). | en_US |
dc.format.extent | 665561 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 | The Rate of Convergence of Fourier Coefficients for Entire Functions of Infinite Order with Application to the Weideman-Cloot Sinh-Mapping for Pseudospectral Computations on an Infinite Interval | en_US |
dc.type | Article | en_US |
dc.rights.robots | IndexNoFollow | en_US |
dc.subject.hlbsecondlevel | Physics | 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, Ocean & Space Science and Laboratory for Scientific Computation, University of Michigan, Ann Arbor, Michigan, USA. | en_US |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/31817/1/0000763.pdf | en_US |
dc.identifier.doi | http://dx.doi.org/10.1006/jcph.1994.1032 | en_US |
dc.identifier.source | Journal of Computational Physics | en_US |
dc.owningcollname | Interdisciplinary and Peer-Reviewed |
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