New algorithms for approximating oscillatory Bessel integrals with Cauchy-type singularities
In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type singularities. By employing the technique of complex line integration, the highly oscillatory Bessel integrals are transformed into oscillatory integr...
Gespeichert in:
| Veröffentlicht in: | Results in applied mathematics Jg. 21; S. 100422 |
|---|---|
| Hauptverfasser: | , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Elsevier B.V
01.02.2024
Elsevier |
| Schlagworte: | |
| ISSN: | 2590-0374, 2590-0374 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type singularities. By employing the technique of complex line integration, the highly oscillatory Bessel integrals are transformed into oscillatory integrals with a Fourier kernel. When the integration interval does not contain zeros, we use Cauchy’s theorem to transform the integration path to the complex plane and then use the Gaussian–Laguerre formula to compute the integral. For cases in which the integration interval contains zeros, we decompose the integral into two parts: the ordinary and the singular integral. We give a stable recursive formula based on Chebyshev polynomials and Bessel functions for ordinary integrals. For singular integrals, we utilize the MeijerG function for efficient computation. Numerical examples verify the effectiveness of the new algorithm and the fast convergence. |
|---|---|
| AbstractList | In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type singularities. By employing the technique of complex line integration, the highly oscillatory Bessel integrals are transformed into oscillatory integrals with a Fourier kernel. When the integration interval does not contain zeros, we use Cauchy’s theorem to transform the integration path to the complex plane and then use the Gaussian–Laguerre formula to compute the integral. For cases in which the integration interval contains zeros, we decompose the integral into two parts: the ordinary and the singular integral. We give a stable recursive formula based on Chebyshev polynomials and Bessel functions for ordinary integrals. For singular integrals, we utilize the MeijerG function for efficient computation. Numerical examples verify the effectiveness of the new algorithm and the fast convergence. |
| ArticleNumber | 100422 |
| Author | Wu, Qinghua Sun, Mengjun |
| Author_xml | – sequence: 1 givenname: Qinghua surname: Wu fullname: Wu, Qinghua email: jackwqh@sina.com – sequence: 2 givenname: Mengjun surname: Sun fullname: Sun, Mengjun email: 459257638@qq.com |
| BookMark | eNp9kMtKAzEUhoMoeOsTuMkLTD2TpDOThQst3kB0ozshnElPasp0UpLx0rc3bUVcuQgJh3wf__mP2X4femLsrIRxCWV1vhhH3-NyLEDIPAElxB47EhMNBcha7f95H7JRSgsAEE1GFRyx10f65NjNQ_TD2zJxFyLH1SqGL7_EwfdzHpL1XYdDiGt-RSlRx30_0Dxil_hnpvgU3-3buhjWK-IpI-8dZpundMoOXP5Fo5_7hL3cXD9P74qHp9v76eVDYWWlhsI51VorXI1SllZr0qK1Oa1CFHVVtXVV1lQB6glA49qJ1rbUUEkBFbUzJ-UJu995ZwEXZhVz9Lg2Ab3ZDkKcG4yDtx0ZJIsTpVpFEvJptHa2butGSCuFnjXZJXcuG0NKkdyvrwSz6dsszLZvs-nb7PrO1MWOorzmh6docmvUW5r5SHbIOfy__DcocY0F |
| Cites_doi | 10.1137/S0036142903431936 10.1016/j.cam.2021.113705 10.1007/BF01934465 10.1016/j.jmaa.2015.11.002 10.1093/imanum/drq035 10.1016/j.cam.2023.115220 10.1016/j.camwa.2016.05.016 10.1016/j.apnum.2012.01.009 10.1090/S0025-5718-1991-1068816-1 10.1016/j.jcp.2010.03.034 10.1016/j.apnum.2019.06.007 10.1155/2021/8021050 10.1007/s11075-015-0033-3 |
| ContentType | Journal Article |
| Copyright | 2023 The Author(s) |
| Copyright_xml | – notice: 2023 The Author(s) |
| DBID | 6I. AAFTH AAYXX CITATION DOA |
| DOI | 10.1016/j.rinam.2023.100422 |
| DatabaseName | ScienceDirect Open Access Titles Elsevier:ScienceDirect:Open Access CrossRef DOAJ Directory of Open Access Journals |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Mathematics |
| EISSN | 2590-0374 |
| ExternalDocumentID | oai_doaj_org_article_aeca544b4e304e3899fc7b7823c329d8 10_1016_j_rinam_2023_100422 S2590037423000687 |
| GroupedDBID | 0SF 6I. AAEDW AAFTH AALRI AAXUO AFTJW AITUG ALMA_UNASSIGNED_HOLDINGS AMRAJ FDB GROUPED_DOAJ M41 NCXOZ OK1 ROL SSZ 0R~ AAYWO AAYXX ADVLN AFJKZ APXCP CITATION |
| ID | FETCH-LOGICAL-c364t-ff4bcc2f7a331c99e92bc3744aa2766b7617e60a95008fb599c19063206ebdf33 |
| IEDL.DBID | DOA |
| ISICitedReferencesCount | 1 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=001166068000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 2590-0374 |
| IngestDate | Fri Oct 03 12:43:49 EDT 2025 Thu Nov 20 00:29:08 EST 2025 Sat Mar 30 16:21:19 EDT 2024 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Keywords | 65D30 Bessel integral Complex integration method Gauss–Laguerre Cauchy-type singularities 65D32 |
| Language | English |
| License | This is an open access article under the CC BY-NC-ND license. |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c364t-ff4bcc2f7a331c99e92bc3744aa2766b7617e60a95008fb599c19063206ebdf33 |
| OpenAccessLink | https://doaj.org/article/aeca544b4e304e3899fc7b7823c329d8 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_aeca544b4e304e3899fc7b7823c329d8 crossref_primary_10_1016_j_rinam_2023_100422 elsevier_sciencedirect_doi_10_1016_j_rinam_2023_100422 |
| PublicationCentury | 2000 |
| PublicationDate | February 2024 2024-02-00 2024-02-01 |
| PublicationDateYYYYMMDD | 2024-02-01 |
| PublicationDate_xml | – month: 02 year: 2024 text: February 2024 |
| PublicationDecade | 2020 |
| PublicationTitle | Results in applied mathematics |
| PublicationYear | 2024 |
| Publisher | Elsevier B.V Elsevier |
| Publisher_xml | – name: Elsevier B.V – name: Elsevier |
| References | Ablowitz, Fokas (b20) 1969 Langdon, Chandler-Wilde (b3) 2006; 43 Lin, Chen, Liu (b5) 2016; 72 Xiang, Cho, Wang, H. (b18) 2011; 31 Abramowitz, Stegun (b6) 1964 Bateman, A. (b21) 1981 Xiang, Fang, Xu (b7) 2016; 435 Liu, Xiang (b8) 2019; 340 Piessens, Branders (b19) 1983; 23 Xu, Xiang (b11) 2016; 72 Kang, Wang, Zhang, Xiang (b14) 2023 Chen (b9) 2012; 62 Nédélec (b4) 2001 I.S., Ryzhik (b15) 2007 Torii (b17) 1991; 56 Wu, Sun (b12) 2021; 2021 Zaman (b13) 2022; 399 Colton, Kress (b2) 1983 J. Ablowitz (b16) 1997 Xu, Fang, Geng (b10) 2019; 145 Asheim, Huybrechs (b1) 2009; 229 Xu (10.1016/j.rinam.2023.100422_b10) 2019; 145 Ablowitz (10.1016/j.rinam.2023.100422_b20) 1969 Torii (10.1016/j.rinam.2023.100422_b17) 1991; 56 Asheim (10.1016/j.rinam.2023.100422_b1) 2009; 229 Xiang (10.1016/j.rinam.2023.100422_b18) 2011; 31 Zaman (10.1016/j.rinam.2023.100422_b13) 2022; 399 Colton (10.1016/j.rinam.2023.100422_b2) 1983 I.S. (10.1016/j.rinam.2023.100422_b15) 2007 J. Ablowitz (10.1016/j.rinam.2023.100422_b16) 1997 Liu (10.1016/j.rinam.2023.100422_b8) 2019; 340 Xu (10.1016/j.rinam.2023.100422_b11) 2016; 72 Xiang (10.1016/j.rinam.2023.100422_b7) 2016; 435 Kang (10.1016/j.rinam.2023.100422_b14) 2023 Langdon (10.1016/j.rinam.2023.100422_b3) 2006; 43 Chen (10.1016/j.rinam.2023.100422_b9) 2012; 62 Bateman (10.1016/j.rinam.2023.100422_b21) 1981 Abramowitz (10.1016/j.rinam.2023.100422_b6) 1964 Wu (10.1016/j.rinam.2023.100422_b12) 2021; 2021 Piessens (10.1016/j.rinam.2023.100422_b19) 1983; 23 Nédélec (10.1016/j.rinam.2023.100422_b4) 2001 Lin (10.1016/j.rinam.2023.100422_b5) 2016; 72 |
| References_xml | – volume: 340 start-page: 251 year: 2019 end-page: 267 ident: b8 article-title: Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels publication-title: Appl Math Comput – year: 1983 ident: b2 article-title: Integral equation methods in scattering theory – volume: 72 start-page: 37 year: 2016 end-page: 56 ident: b11 article-title: On the evaluation of highly oscillatory finite Hankel transform using special functions publication-title: Numer Algorithms – volume: 145 start-page: 121 year: 2019 end-page: 132 ident: b10 article-title: Fast computation of Bessel transform with highly oscillatory integrands publication-title: Appl Numer Math – volume: 435 start-page: 1210 year: 2016 end-page: 1228 ident: b7 article-title: On uniform approximations to hypersingular finite-part integrals publication-title: J Math Anal Appl – year: 1969 ident: b20 article-title: The special functions and their approximations, vol. 2 – year: 1997 ident: b16 article-title: Complex variables: Introduction and applications – volume: 31 start-page: 1281 year: 2011 end-page: 1314 ident: b18 article-title: Clenshaw-Curtis-Filon-type methods for highly oscillatory bessel transforms and applications publication-title: IMA J Numer Anal – year: 1964 ident: b6 article-title: Handbook of mathematical functions – volume: 2021 year: 2021 ident: b12 article-title: Numerical steepest descent method for Hankel type of hypersingular oscillatory integrals in electromagnetic scattering problems publication-title: Adv Math Phys – volume: 399 year: 2022 ident: b13 article-title: New algorithms for approximation of Bessel transforms with high frequency parameter publication-title: J Comput Appl Math – year: 2001 ident: b4 article-title: Acoustic and electromagnetic equations – year: 2023 ident: b14 article-title: Efficient computation of oscillatory Bessel transforms with a singularity of Cauchy type publication-title: J Comput Appl Math – volume: 229 start-page: 5357 year: 2009 end-page: 5372 ident: b1 article-title: Local solutions to high frequency 2D scattering problems publication-title: J Comput Phys – volume: 43 start-page: 2450 year: 2006 end-page: 2477 ident: b3 article-title: A wavenumber independent boundary element method for an acoustic scattering problem publication-title: SIAM J Numer Anal – volume: 62 start-page: 636 year: 2012 end-page: 648 ident: b9 article-title: Numerical approximations to integrals with a highly oscillatory Bessel kernel publication-title: Appl Numer Math – volume: 56 start-page: 741 year: 1991 end-page: 754 ident: b17 article-title: An automatic quadrature for Cauchy principal value integrals publication-title: Math Comp – year: 1981 ident: b21 article-title: Higher transcendental functions, vol. I – volume: 72 start-page: 555 year: 2016 end-page: 567 ident: b5 article-title: Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions publication-title: Comput Math Appl – year: 2007 ident: b15 article-title: Table of integrals, series, and products – volume: 23 start-page: 370 year: 1983 end-page: 381 ident: b19 article-title: Modified Clenshaw–Curtis method for the computation of Bessel function integrals publication-title: BIT Numer Math – volume: 43 start-page: 2450 year: 2006 ident: 10.1016/j.rinam.2023.100422_b3 article-title: A wavenumber independent boundary element method for an acoustic scattering problem publication-title: SIAM J Numer Anal doi: 10.1137/S0036142903431936 – volume: 399 issn: 0377-0427 year: 2022 ident: 10.1016/j.rinam.2023.100422_b13 article-title: New algorithms for approximation of Bessel transforms with high frequency parameter publication-title: J Comput Appl Math doi: 10.1016/j.cam.2021.113705 – volume: 23 start-page: 370 year: 1983 ident: 10.1016/j.rinam.2023.100422_b19 article-title: Modified Clenshaw–Curtis method for the computation of Bessel function integrals publication-title: BIT Numer Math doi: 10.1007/BF01934465 – volume: 435 start-page: 1210 issue: 2 year: 2016 ident: 10.1016/j.rinam.2023.100422_b7 article-title: On uniform approximations to hypersingular finite-part integrals publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2015.11.002 – volume: 31 start-page: 1281 issue: 4 year: 2011 ident: 10.1016/j.rinam.2023.100422_b18 article-title: Clenshaw-Curtis-Filon-type methods for highly oscillatory bessel transforms and applications publication-title: IMA J Numer Anal doi: 10.1093/imanum/drq035 – year: 2023 ident: 10.1016/j.rinam.2023.100422_b14 article-title: Efficient computation of oscillatory Bessel transforms with a singularity of Cauchy type publication-title: J Comput Appl Math doi: 10.1016/j.cam.2023.115220 – year: 1981 ident: 10.1016/j.rinam.2023.100422_b21 – volume: 72 start-page: 555 year: 2016 ident: 10.1016/j.rinam.2023.100422_b5 article-title: Fast simulation of multi-dimensional wave problems by the sparse scheme of the method of fundamental solutions publication-title: Comput Math Appl doi: 10.1016/j.camwa.2016.05.016 – volume: 62 start-page: 636 issue: 5 year: 2012 ident: 10.1016/j.rinam.2023.100422_b9 article-title: Numerical approximations to integrals with a highly oscillatory Bessel kernel publication-title: Appl Numer Math doi: 10.1016/j.apnum.2012.01.009 – year: 2007 ident: 10.1016/j.rinam.2023.100422_b15 – volume: 56 start-page: 741 issue: 194 year: 1991 ident: 10.1016/j.rinam.2023.100422_b17 article-title: An automatic quadrature for Cauchy principal value integrals publication-title: Math Comp doi: 10.1090/S0025-5718-1991-1068816-1 – year: 1983 ident: 10.1016/j.rinam.2023.100422_b2 – volume: 229 start-page: 5357 year: 2009 ident: 10.1016/j.rinam.2023.100422_b1 article-title: Local solutions to high frequency 2D scattering problems publication-title: J Comput Phys doi: 10.1016/j.jcp.2010.03.034 – volume: 145 start-page: 121 issue: 11 year: 2019 ident: 10.1016/j.rinam.2023.100422_b10 article-title: Fast computation of Bessel transform with highly oscillatory integrands publication-title: Appl Numer Math doi: 10.1016/j.apnum.2019.06.007 – year: 2001 ident: 10.1016/j.rinam.2023.100422_b4 – volume: 2021 issn: 1687-9120 year: 2021 ident: 10.1016/j.rinam.2023.100422_b12 article-title: Numerical steepest descent method for Hankel type of hypersingular oscillatory integrals in electromagnetic scattering problems publication-title: Adv Math Phys doi: 10.1155/2021/8021050 – volume: 340 start-page: 251 year: 2019 ident: 10.1016/j.rinam.2023.100422_b8 article-title: Clenshaw-Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels publication-title: Appl Math Comput – volume: 72 start-page: 37 issue: 1 year: 2016 ident: 10.1016/j.rinam.2023.100422_b11 article-title: On the evaluation of highly oscillatory finite Hankel transform using special functions publication-title: Numer Algorithms doi: 10.1007/s11075-015-0033-3 – year: 1997 ident: 10.1016/j.rinam.2023.100422_b16 – year: 1964 ident: 10.1016/j.rinam.2023.100422_b6 – year: 1969 ident: 10.1016/j.rinam.2023.100422_b20 |
| SSID | ssj0002810140 |
| Score | 2.2527776 |
| Snippet | In this paper, we present an efficient numerical algorithm for approximating integrals involving highly oscillatory Bessel functions with Cauchy-type... |
| SourceID | doaj crossref elsevier |
| SourceType | Open Website Index Database Publisher |
| StartPage | 100422 |
| SubjectTerms | Bessel integral Cauchy-type singularities Complex integration method Gauss–Laguerre |
| Title | New algorithms for approximating oscillatory Bessel integrals with Cauchy-type singularities |
| URI | https://dx.doi.org/10.1016/j.rinam.2023.100422 https://doaj.org/article/aeca544b4e304e3899fc7b7823c329d8 |
| Volume | 21 |
| WOSCitedRecordID | wos001166068000001&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 2590-0374 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0002810140 issn: 2590-0374 databaseCode: DOA dateStart: 20190101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV07T8MwELYQYoAB8RTlJQ-MRAT7bMcjrahYqBhA6oAU2Y7Th0qKmhbBv8d2kiossDBkiZxz9F2U-3w-f4fQFXAKwsYyMoLlESTAImmIjrRIpHX0HyzNQrMJMRgkw6F8arX68jVhlTxwBdyNskYxAO0eit3llge5Ec4SoYYSmYVjvrGQrcXUNKSMfA_auJEZCgVdi0mh_NlzQn1pABDyIxQFxf5WRGpFmf4e2q3pIb6rXmsfbdjiAO08rrVVy0P06v5LWM1Gc7esH7-V2LFOHJTBPyd-SDHCXp_Seddvn-Ou1waf4VoVYlZin3jFPbUy46_I51-xTxb4WtQgrXqEXvr3z72HqO6REBnKYRnlOWhjSC4UpbdGSiuJNlQAKEUE51o4hmJ5rCRzwT7XTErjKACnJOZWZzmlx2izmBf2BGESGwOagkOcAcm0tpxRT4dAJZZkrIOuG7jS90oKI21qxKZpQDf16KYVuh3U9ZCuh3od63DDeTetvZv-5d0O4o1D0poSVKHemZr8Nvvpf8x-hradSaiKtM_R5nKxshdoy3wsJ-XiMnxx34w13Fg |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=New+algorithms+for+approximating+oscillatory+Bessel+integrals+with+Cauchy-type+singularities&rft.jtitle=Results+in+applied+mathematics&rft.au=Qinghua+Wu&rft.au=Mengjun+Sun&rft.date=2024-02-01&rft.pub=Elsevier&rft.eissn=2590-0374&rft.volume=21&rft.spage=100422&rft_id=info:doi/10.1016%2Fj.rinam.2023.100422&rft.externalDBID=DOA&rft.externalDocID=oai_doaj_org_article_aeca544b4e304e3899fc7b7823c329d8 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=2590-0374&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=2590-0374&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=2590-0374&client=summon |