Highly oscillatory quadrature: The story so far
The last few years have witnessed substantive developments in the computation of highly oscillatory integrals in one or more dimensions. The availability of new asymptotic expansions and a Stokes-type theorem allow for a comprehensive analysis of a number of old (although enhanced) and new quadratur...
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| Format: | Conference item |
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2006
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| _version_ | 1797105882563084288 |
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| author | Iserles, A Norsett, S Olver, S |
| author_facet | Iserles, A Norsett, S Olver, S |
| author_sort | Iserles, A |
| collection | OXFORD |
| description | The last few years have witnessed substantive developments in the computation of highly oscillatory integrals in one or more dimensions. The availability of new asymptotic expansions and a Stokes-type theorem allow for a comprehensive analysis of a number of old (although enhanced) and new quadrature techniques: the asymptotic, Filon-type and Levin-type methods. All these methods share the surprising property that their accuracy increases with growing oscillation. These developments are described in a unified fashion, taking the multivariate integral f(Omega) f (chi)e(iwg(chi))dV as our point of departure. |
| first_indexed | 2024-03-07T06:53:42Z |
| format | Conference item |
| id | oxford-uuid:fd67bd7f-573e-4958-acfe-e3c77d5b52b1 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:53:42Z |
| publishDate | 2006 |
| record_format | dspace |
| spelling | oxford-uuid:fd67bd7f-573e-4958-acfe-e3c77d5b52b12022-03-27T13:28:34ZHighly oscillatory quadrature: The story so farConference itemhttp://purl.org/coar/resource_type/c_5794uuid:fd67bd7f-573e-4958-acfe-e3c77d5b52b1Symplectic Elements at Oxford2006Iserles, ANorsett, SOlver, SThe last few years have witnessed substantive developments in the computation of highly oscillatory integrals in one or more dimensions. The availability of new asymptotic expansions and a Stokes-type theorem allow for a comprehensive analysis of a number of old (although enhanced) and new quadrature techniques: the asymptotic, Filon-type and Levin-type methods. All these methods share the surprising property that their accuracy increases with growing oscillation. These developments are described in a unified fashion, taking the multivariate integral f(Omega) f (chi)e(iwg(chi))dV as our point of departure. |
| spellingShingle | Iserles, A Norsett, S Olver, S Highly oscillatory quadrature: The story so far |
| title | Highly oscillatory quadrature: The story so far |
| title_full | Highly oscillatory quadrature: The story so far |
| title_fullStr | Highly oscillatory quadrature: The story so far |
| title_full_unstemmed | Highly oscillatory quadrature: The story so far |
| title_short | Highly oscillatory quadrature: The story so far |
| title_sort | highly oscillatory quadrature the story so far |
| work_keys_str_mv | AT iserlesa highlyoscillatoryquadraturethestorysofar AT norsetts highlyoscillatoryquadraturethestorysofar AT olvers highlyoscillatoryquadraturethestorysofar |