Moment-free numerical approximation of highly oscillatory integrals with stationary points
This article presents a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is c...
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| Format: | Journal article |
| Language: | English |
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2007
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| _version_ | 1797085744226893824 |
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| author | Olver, S |
| author_facet | Olver, S |
| author_sort | Olver, S |
| collection | OXFORD |
| description | This article presents a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an alternate approximation method that has similar asymptotic behaviour, but with significantly greater accuracy. This approximation method does not require moments. © 2007 Cambridge University Press. |
| first_indexed | 2024-03-07T02:12:18Z |
| format | Journal article |
| id | oxford-uuid:a1114c55-d27b-41fc-ae9d-2dcf39cc6b11 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T02:12:18Z |
| publishDate | 2007 |
| record_format | dspace |
| spelling | oxford-uuid:a1114c55-d27b-41fc-ae9d-2dcf39cc6b112022-03-27T02:10:16ZMoment-free numerical approximation of highly oscillatory integrals with stationary pointsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:a1114c55-d27b-41fc-ae9d-2dcf39cc6b11EnglishSymplectic Elements at Oxford2007Olver, SThis article presents a method for the numerical quadrature of highly oscillatory integrals with stationary points. We begin with the derivation of a new asymptotic expansion, which has the property that the accuracy improves as the frequency of oscillations increases. This asymptotic expansion is closely related to the method of stationary phase, but presented in a way that allows the derivation of an alternate approximation method that has similar asymptotic behaviour, but with significantly greater accuracy. This approximation method does not require moments. © 2007 Cambridge University Press. |
| spellingShingle | Olver, S Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title | Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title_full | Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title_fullStr | Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title_full_unstemmed | Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title_short | Moment-free numerical approximation of highly oscillatory integrals with stationary points |
| title_sort | moment free numerical approximation of highly oscillatory integrals with stationary points |
| work_keys_str_mv | AT olvers momentfreenumericalapproximationofhighlyoscillatoryintegralswithstationarypoints |