{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T12:54:39Z","timestamp":1740142479335,"version":"3.37.3"},"reference-count":19,"publisher":"Springer Science and Business Media LLC","issue":"3","license":[{"start":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T00:00:00Z","timestamp":1591920000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T00:00:00Z","timestamp":1591920000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"publisher","award":["2015A030313615"],"award-info":[{"award-number":["2015A030313615"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Comp. Appl. Math."],"published-print":{"date-parts":[[2020,9]]},"DOI":"10.1007\/s40314-020-01193-9","type":"journal-article","created":{"date-parts":[[2020,6,12]],"date-time":"2020-06-12T15:03:42Z","timestamp":1591974222000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerical approximations of highly oscillatory Hilbert transforms"],"prefix":"10.1007","volume":"39","author":[{"given":"Ruyun","family":"Chen","sequence":"first","affiliation":[]},{"given":"Di","family":"Yu","sequence":"additional","affiliation":[]},{"given":"Juan","family":"Chen","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,6,12]]},"reference":[{"key":"1193_CR1","volume-title":"Handbook of mathematical functions","author":"M Abramowitz","year":"1964","unstructured":"Abramowitz M, Stegun IA (1964) Handbook of mathematical functions. National Bureau of Standards, Washington, D.C"},{"key":"1193_CR2","volume-title":"Mathematical methods for physicists","author":"G Arfken","year":"1985","unstructured":"Arfken G (1985) Mathematical methods for physicists, 3rd edn. Academic Press, Orlando","edition":"3"},{"key":"1193_CR3","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1137\/S1064827503428539","volume":"27","author":"G Bao","year":"2005","unstructured":"Bao G, Sun W (2005) A fast algorithm for the electromagnetic scattering form a large cavity. SIAM J Sci Comput 27:553\u2013574","journal-title":"SIAM J Sci Comput"},{"key":"1193_CR4","doi-asserted-by":"publisher","first-page":"701","DOI":"10.1080\/00207160.2012.655688","volume":"89","author":"RY Chen","year":"2012","unstructured":"Chen RY (2012) Numerical analysis for Cauchy principal value integrals of oscillatory kind. Int J Comput Math 89:701\u2013710","journal-title":"Int J Comput Math"},{"key":"1193_CR5","doi-asserted-by":"publisher","first-page":"21","DOI":"10.1007\/s10440-012-9709-z","volume":"123","author":"RY Chen","year":"2013","unstructured":"Chen RY (2013) Fast integration for Cauchy principal value integrals of oscillatory kind. Acta Appl Math 123:21\u201330","journal-title":"Acta Appl Math"},{"key":"1193_CR6","first-page":"494","volume":"227","author":"RY Chen","year":"2014","unstructured":"Chen RY (2014) Fast computation of a class of highly oscillatory integrals. Appl Math Comput 227:494\u2013501","journal-title":"Appl Math Comput"},{"key":"1193_CR7","volume-title":"Methods of numerical integration","author":"PJ Davis","year":"1984","unstructured":"Davis PJ, Rabinowitz P (1984) Methods of numerical integration, 2nd edn. Academic Press, London","edition":"2"},{"key":"1193_CR8","doi-asserted-by":"publisher","first-page":"38","DOI":"10.1017\/S0370164600026262","volume":"49","author":"LNG Filon","year":"1928","unstructured":"Filon LNG (1928) On a quadrature formula for trigonometric integrals. Pro R Soc Edinburgh 49:38\u201347","journal-title":"Pro R Soc Edinburgh"},{"key":"1193_CR9","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.cam.2019.02.012","volume":"358","author":"T Hasegawa","year":"2019","unstructured":"Hasegawa T, Sugiura H (2019) Uniform approximation to finite Hilbert transform of oscillatory functions and its algorithm. J Comput Appl Math 358:95\u2013100","journal-title":"J Comput Appl Math"},{"key":"1193_CR10","doi-asserted-by":"publisher","first-page":"1383","DOI":"10.1098\/rspa.2004.1401","volume":"461","author":"A Iserles","year":"2005","unstructured":"Iserles A, N\u00f8rsett SP (2005) Efficient quadrature of highly-oscillatory integrals using derivatives. Proc R Soc Lond Ser A Math Phys Eng Sci 461:1383\u20131399","journal-title":"Proc R Soc Lond Ser A Math Phys Eng Sci"},{"key":"1193_CR11","doi-asserted-by":"publisher","first-page":"531","DOI":"10.1090\/S0025-5718-1982-0645668-7","volume":"38","author":"D Levin","year":"1982","unstructured":"Levin D (1982) Procedures for computing one- and two-dimensional integrals of functions with rapid irregular oscillations. Math Comput 38:531\u2013538","journal-title":"Math Comput"},{"issue":"2","key":"1193_CR12","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1093\/imanum\/dri040","volume":"26","author":"S Olver","year":"2006","unstructured":"Olver S (2006) Moments-free numerical integration of highly oscillatory functions. IMA J Numer Anal 26(2):213\u2013227","journal-title":"IMA J Numer Anal"},{"key":"1193_CR13","first-page":"1886","volume":"215","author":"HY Wang","year":"2009","unstructured":"Wang HY, Xiang SH (2009) Uniform approximations to Cauchy principal value integrals of oscillatory functions. Appl Math Comput 215:1886\u20131894","journal-title":"Appl Math Comput"},{"key":"1193_CR14","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1016\/j.cam.2009.12.007","volume":"234","author":"HY Wang","year":"2010","unstructured":"Wang HY, Xiang SH (2010) On the evaluation of Cauchy principal value integrals of oscillatory functions. J Comput Appl Math 234:95\u2013100","journal-title":"J Comput Appl Math"},{"key":"1193_CR15","doi-asserted-by":"publisher","first-page":"709","DOI":"10.1007\/s00211-012-0501-9","volume":"123","author":"HY Wang","year":"2013","unstructured":"Wang HY, Zhang L, Huybrechs D (2013) Asymptotic expansions and fast computation of oscillatory Hilbert transforms. Numer Math 123:709\u2013743","journal-title":"Numer Math"},{"key":"1193_CR16","doi-asserted-by":"publisher","first-page":"92","DOI":"10.1137\/0511007","volume":"11","author":"R Wong","year":"1980","unstructured":"Wong R (1980) Asymptotic expansion of the Hilbert transform. SIAM J Math Anal 11:92\u201399","journal-title":"SIAM J Math Anal"},{"key":"1193_CR17","doi-asserted-by":"publisher","first-page":"829","DOI":"10.1090\/S0025-5718-09-02279-0","volume":"79","author":"SH Xiang","year":"2010","unstructured":"Xiang SH, Wang HY (2010) Fast integration of highly oscillatory integrals with exotic oscillators. Math Comput 79:829\u2013844","journal-title":"Math Comput"},{"issue":"2","key":"1193_CR18","doi-asserted-by":"publisher","first-page":"1210","DOI":"10.1016\/j.jmaa.2015.11.002","volume":"435","author":"SH Xiang","year":"2016","unstructured":"Xiang SH, Fang CH, Xu ZH (2016) On uniform approximations to hypersingular finite-part integrals. J Math Anal Appl 435(2):1210\u20131228","journal-title":"J Math Anal Appl"},{"key":"1193_CR19","doi-asserted-by":"publisher","first-page":"979","DOI":"10.11650\/tjm\/170904","volume":"22","author":"ZH Xu","year":"2018","unstructured":"Xu ZH (2018) On the numerical quadrature of weakly singular oscillatory integral and its fast implementation. Taiwan J Math 22:979\u20131000","journal-title":"Taiwan J Math"}],"container-title":["Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01193-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s40314-020-01193-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s40314-020-01193-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,6,11]],"date-time":"2021-06-11T23:17:35Z","timestamp":1623453455000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s40314-020-01193-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,6,12]]},"references-count":19,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2020,9]]}},"alternative-id":["1193"],"URL":"https:\/\/doi.org\/10.1007\/s40314-020-01193-9","relation":{},"ISSN":["2238-3603","1807-0302"],"issn-type":[{"type":"print","value":"2238-3603"},{"type":"electronic","value":"1807-0302"}],"subject":[],"published":{"date-parts":[[2020,6,12]]},"assertion":[{"value":"4 December 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 May 2020","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 May 2020","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 June 2020","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"180"}}