Computing Complex Airy Functions by Numerical Quadrature
Integral representations are considered of solutions of the Airy differential equation w′′−zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations...
Uloženo v:
| Vydáno v: | Numerical algorithms Ročník 30; číslo 1; s. 11 - 23 |
|---|---|
| Hlavní autoři: | , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
New York
Springer Nature B.V
01.05.2002
|
| Témata: | |
| ISSN: | 1017-1398, 1572-9265 |
| On-line přístup: | Získat plný text |
| Tagy: |
Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
|
| Abstract | Integral representations are considered of solutions of the Airy differential equation w′′−zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions. |
|---|---|
| AbstractList | Integral representations are considered of solutions of the Airy differential equation w′′−zw=0 for computing Airy functions for complex values of z. In a first method contour integral representations of the Airy functions are written as non-oscillating integrals for obtaining stable representations, which are evaluated by the trapezoidal rule. In a second method an integral representation is evaluated by using generalized Gauss–Laguerre quadrature; this approach provides a fast method for computing Airy functions to a predetermined accuracy. Comparisons are made with well-known algorithms of Amos, designed for computing Bessel functions of complex argument. Several discrepancies with Amos' code are detected, and it is pointed out for which regions of the complex plane Amos' code is less accurate than the quadrature algorithms. Hints are given in order to build reliable software for complex Airy functions. |
| Author | Temme, Nico M. Segura, Javier Gil, Amparo |
| Author_xml | – sequence: 1 givenname: Amparo surname: Gil fullname: Gil, Amparo – sequence: 2 givenname: Javier surname: Segura fullname: Segura, Javier – sequence: 3 givenname: Nico M. surname: Temme fullname: Temme, Nico M. |
| BookMark | eNp1kMFLwzAYxYNMcJuevRY81-VLmjTxVoZTYSiCnkOapJLRtTNJwf73dsyLgqf3Du_3fby3QLOu7xxC14BvARO6qu4AA-OUC8IYYWdoDqwkuSSczSaPocyBSnGBFjHuMAaMSTlHYt3vD0Py3Ud2dK37yiofxmwzdCb5votZPWbPw94Fb3SbvQ7aBp2G4C7ReaPb6K5-dIneN_dv68d8-_LwtK62uaGUptzWWJfUmoaXsixqZjk4C2AIJgwIxkUjKXBJwDJhmrphmkirTYELKTlIS5fo5nT3EPrPwcWkdv0QuumlIhJEISRwMaXYKWVCH2NwjTI-6WOBFLRvFWB1HElV6tdIE7f6wx2C3-sw_kt8A-PSaIA |
| CitedBy_id | crossref_primary_10_1145_592843_592847 crossref_primary_10_1145_1916461_1916471 crossref_primary_10_1137_21M1401590 crossref_primary_10_1017_jfm_2017_889 crossref_primary_10_1016_j_scico_2013_11_004 crossref_primary_10_1016_S0377_0427_02_00608_8 crossref_primary_10_1023_A_1025524324969 crossref_primary_10_1016_j_cam_2020_112717 crossref_primary_10_1145_569147_569150 crossref_primary_10_1016_j_cpc_2017_01_010 crossref_primary_10_1016_j_apnum_2023_11_017 crossref_primary_10_1145_1377596_1377602 crossref_primary_10_1007_s00211_009_0264_0 crossref_primary_10_1137_130932132 crossref_primary_10_1088_1402_4896_aceba3 |
| Cites_doi | 10.1023/A:1021974203359 10.1090/S0025-5718-00-01268-0 10.1002/9781118032572 10.1016/0021-9991(92)90279-8 10.1016/0021-9991(79)90062-7 10.1017/S0305004100024786 10.1145/7921.214331 10.1090/psapm/048/1314844 |
| ContentType | Journal Article |
| Copyright | Kluwer Academic Publishers 2002. |
| Copyright_xml | – notice: Kluwer Academic Publishers 2002. |
| DBID | AAYXX CITATION 8FE 8FG ABJCF AFKRA ARAPS AZQEC BENPR BGLVJ CCPQU DWQXO GNUQQ HCIFZ JQ2 K7- L6V M7S P62 PHGZM PHGZT PKEHL PQEST PQGLB PQQKQ PQUKI PRINS PTHSS |
| DOI | 10.1023/A:1015636825525 |
| DatabaseName | CrossRef ProQuest SciTech Collection ProQuest Technology Collection Materials Science & Engineering Collection ProQuest Central UK/Ireland Advanced Technologies & Computer Science Collection ProQuest Central Essentials ProQuest Central Technology collection ProQuest One Community College ProQuest Central ProQuest Central Student SciTech Premium Collection ProQuest Computer Science Collection Computer Science Database ProQuest Engineering Collection Engineering Database ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Premium ProQuest One Academic ProQuest One Academic Middle East (New) ProQuest One Academic Eastern Edition (DO NOT USE) ProQuest One Applied & Life Sciences ProQuest One Academic (retired) ProQuest One Academic UKI Edition ProQuest Central China Engineering collection |
| DatabaseTitle | CrossRef Computer Science Database ProQuest Central Student Technology Collection ProQuest One Academic Middle East (New) ProQuest Advanced Technologies & Aerospace Collection ProQuest Central Essentials ProQuest Computer Science Collection SciTech Premium Collection ProQuest One Community College ProQuest Central China ProQuest Central ProQuest One Applied & Life Sciences ProQuest Engineering Collection ProQuest Central Korea ProQuest Central (New) Engineering Collection Advanced Technologies & Aerospace Collection Engineering Database ProQuest One Academic Eastern Edition ProQuest Technology Collection ProQuest SciTech Collection ProQuest One Academic UKI Edition Materials Science & Engineering Collection ProQuest One Academic ProQuest One Academic (New) |
| DatabaseTitleList | Computer Science Database |
| Database_xml | – sequence: 1 dbid: BENPR name: ProQuest Central url: https://www.proquest.com/central sourceTypes: Aggregation Database |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Applied Sciences Mathematics |
| EISSN | 1572-9265 |
| EndPage | 23 |
| ExternalDocumentID | 10_1023_A_1015636825525 |
| GroupedDBID | -Y2 -~C .86 .DC .VR 06D 0R~ 0VY 123 1N0 1SB 2.D 203 29N 2J2 2JN 2JY 2KG 2KM 2LR 2P1 2VQ 2~H 30V 4.4 406 408 409 40D 40E 5QI 5VS 67Z 6NX 8TC 8UJ 95- 95. 95~ 96X AAAVM AABHQ AACDK AAHNG AAIAL AAJBT AAJKR AANZL AAOBN AAPKM AARHV AARTL AASML AATNV AATVU AAUYE AAWCG AAYIU AAYQN AAYTO AAYXX ABAKF ABBBX ABBRH ABBXA ABDBE ABDZT ABECU ABFSG ABFTD ABFTV ABHLI ABHQN ABJCF ABJNI ABJOX ABKCH ABKTR ABMNI ABMQK ABNWP ABQBU ABQSL ABRTQ ABSXP ABTEG ABTHY ABTKH ABTMW ABULA ABWNU ABXPI ACAOD ACBXY ACDTI ACGFS ACHSB ACHXU ACIWK ACKNC ACMDZ ACMLO ACOKC ACOMO ACPIV ACSNA ACSTC ACZOJ ADHHG ADHIR ADHKG ADIMF ADKNI ADKPE ADRFC ADTPH ADURQ ADYFF ADZKW AEBTG AEFIE AEFQL AEGAL AEGNC AEJHL AEJRE AEKMD AEMSY AENEX AEOHA AEPYU AETLH AEVLU AEXYK AEZWR AFBBN AFDZB AFEXP AFFHD AFGCZ AFHIU AFKRA AFLOW AFOHR AFQWF AFWTZ AFZKB AGAYW AGDGC AGGDS AGJBK AGMZJ AGQEE AGQMX AGQPQ AGRTI AGWIL AGWZB AGYKE AHAVH AHBYD AHKAY AHPBZ AHSBF AHWEU AHYZX AIAKS AIGIU AIIXL AILAN AITGF AIXLP AJBLW AJRNO AJZVZ ALMA_UNASSIGNED_HOLDINGS ALWAN AMKLP AMXSW AMYLF AMYQR AOCGG ARAPS ARMRJ ASPBG ATHPR AVWKF AXYYD AYFIA AYJHY AZFZN B-. BA0 BBWZM BDATZ BENPR BGLVJ BGNMA BSONS CAG CCPQU CITATION COF CS3 CSCUP DDRTE DL5 DNIVK DPUIP DU5 EBLON EBS EIOEI EJD ESBYG FEDTE FERAY FFXSO FIGPU FINBP FNLPD FRRFC FSGXE FWDCC GGCAI GGRSB GJIRD GNWQR GQ7 GQ8 GXS H13 HCIFZ HF~ HG5 HG6 HMJXF HQYDN HRMNR HVGLF HZ~ I09 IHE IJ- IKXTQ ITM IWAJR IXC IZIGR IZQ I~X I~Z J-C J0Z JBSCW JCJTX JZLTJ K7- KDC KOV KOW LAK LLZTM M4Y M7S MA- N2Q N9A NB0 NDZJH NPVJJ NQJWS NU0 O9- O93 O9G O9I O9J OAM OVD P19 P2P P9O PF0 PHGZM PHGZT PQGLB PT4 PT5 PTHSS QOK QOS R4E R89 R9I RHV RNI RNS ROL RPX RSV RZC RZE RZK S16 S1Z S26 S27 S28 S3B SAP SCJ SCLPG SCO SDH SDM SHX SISQX SJYHP SNE SNPRN SNX SOHCF SOJ SPISZ SRMVM SSLCW STPWE SZN T13 T16 TEORI TSG TSK TSV TUC U2A UG4 UOJIU UTJUX UZXMN VC2 VFIZW VOH W23 W48 WK8 YLTOR Z45 ZMTXR ZY4 ~EX 8FE 8FG AZQEC DWQXO GNUQQ JQ2 L6V P62 PKEHL PQEST PQQKQ PQUKI PRINS |
| ID | FETCH-LOGICAL-c333t-db0a73dcf67974b5d61ed11c202512004f9316921d58cfbf5a29dac40499619d3 |
| IEDL.DBID | BENPR |
| ISICitedReferencesCount | 17 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000175782800002&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| ISSN | 1017-1398 |
| IngestDate | Thu Nov 27 09:41:31 EST 2025 Tue Nov 18 19:41:53 EST 2025 Sat Nov 29 07:48:58 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 1 |
| Language | English |
| License | https://www.springernature.com/gp/researchers/text-and-data-mining |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c333t-db0a73dcf67974b5d61ed11c202512004f9316921d58cfbf5a29dac40499619d3 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2918489168 |
| PQPubID | 2043837 |
| PageCount | 13 |
| ParticipantIDs | proquest_journals_2918489168 crossref_citationtrail_10_1023_A_1015636825525 crossref_primary_10_1023_A_1015636825525 |
| PublicationCentury | 2000 |
| PublicationDate | 2002-05-01 |
| PublicationDateYYYYMMDD | 2002-05-01 |
| PublicationDate_xml | – month: 05 year: 2002 text: 2002-05-01 day: 01 |
| PublicationDecade | 2000 |
| PublicationPlace | New York |
| PublicationPlace_xml | – name: New York |
| PublicationTitle | Numerical algorithms |
| PublicationYear | 2002 |
| Publisher | Springer Nature B.V |
| Publisher_xml | – name: Springer Nature B.V |
| References | R. Wong (397515_CR13) 1989 A. Gil (397515_CR5) 2001; 70 397515_CR6 397515_CR8 N.M. Temme (397515_CR12) 1996 (397515_CR1) 1964 R.M. Corless (397515_CR3) 1992; 99 F.W.J. Olver (397515_CR10) 1974 E.T. Goodwin (397515_CR7) 1949; 45 W. Gautschi (397515_CR4) 2002; 42 Y.L. Luke (397515_CR9) 1969 Z. Schulten (397515_CR11) 1979; 31 D.E. Amos (397515_CR2) 1986; 12 |
| References_xml | – volume-title: Asymptotic Approximations of Integrals year: 1989 ident: 397515_CR13 – volume: 42 start-page: 110 year: 2002 ident: 397515_CR4 publication-title: BIT doi: 10.1023/A:1021974203359 – volume: 70 start-page: 1183 year: 2001 ident: 397515_CR5 publication-title: Math. Comput. doi: 10.1090/S0025-5718-00-01268-0 – volume-title: Special Functions: An Introduction to the Classical Functions of Mathematical Physics year: 1996 ident: 397515_CR12 doi: 10.1002/9781118032572 – ident: 397515_CR6 – volume: 99 start-page: 106 year: 1992 ident: 397515_CR3 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(92)90279-8 – volume-title: The Special Functions and Their Approximations, Vol. I-II year: 1969 ident: 397515_CR9 – volume-title: Handbook of Mathematical Functions year: 1964 ident: 397515_CR1 – volume: 31 start-page: 60 year: 1979 ident: 397515_CR11 publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(79)90062-7 – volume: 45 start-page: 241 year: 1949 ident: 397515_CR7 publication-title: Cambridge Phil. Soc. Proc. doi: 10.1017/S0305004100024786 – volume: 12 start-page: 265 year: 1986 ident: 397515_CR2 publication-title: ACM Trans. Math. Softw. doi: 10.1145/7921.214331 – volume-title: Asymptotics and Special Functions year: 1974 ident: 397515_CR10 – ident: 397515_CR8 doi: 10.1090/psapm/048/1314844 |
| SSID | ssj0010027 |
| Score | 1.6740236 |
| Snippet | Integral representations are considered of solutions of the Airy differential equation w′′−zw=0 for computing Airy functions for complex values of z. In a... |
| SourceID | proquest crossref |
| SourceType | Aggregation Database Enrichment Source Index Database |
| StartPage | 11 |
| SubjectTerms | Airy function Algorithms Bessel functions Computation Differential equations Quadratures Representations |
| Title | Computing Complex Airy Functions by Numerical Quadrature |
| URI | https://www.proquest.com/docview/2918489168 |
| Volume | 30 |
| WOSCitedRecordID | wos000175782800002&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: PRVAVX databaseName: Springer Nature - Connect here FIRST to enable access customDbUrl: eissn: 1572-9265 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0010027 issn: 1017-1398 databaseCode: RSV dateStart: 19970101 isFulltext: true titleUrlDefault: https://link.springer.com/search?facet-content-type=%22Journal%22 providerName: Springer Nature |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV3PT8IwFH5R8KAHUdSIIunBg5epW9nWngwaiImRIKjhtnTtmpAQQAZG_ntft4Jiohcvy5L9yLL38-trvg_gnHPFqZaeg-2xcuoyEI6QCYa7zzSmQhq7SmRiE2G7zfp93rELbqndVrnMiVmiVmNp1sivPI5YhGEzw24mb45RjTLTVSuhsQlFw1SGfl68bbY73dUcwaCubN6JuRh7HfaD3AfBCw0QI_lGKft7XVpPy1mtaZX--5V7sGu7TNLI3WIfNpJRGUq24yQ2ntMy7DyuWFvTA2C5xAMWM2LOhskHaQymC9LC2pe5J4kXpD3PZzxD8jQXKmdkPoSXVvP57t6xygqOpJTOHBVfi5AqqYMQ8UTsq8BNlOtKzyAOEzeaUzfgnqt8JnWsfeFxJWTd4CNEXIoeQWE0HiXHQBIaqMSTkhpoiaaONdXcV_jGwGVKhBW4XP7XSFracaN-MYyy8bdHo0a0ZogKXKwemOSMG7_fWl1aIbKhl0ZfJjj5-_IpbGfSLtnuxSoUZtN5cgZb8n02SKc160k12HwInZrZEtrDY7f3-gnl_NGI |
| linkProvider | ProQuest |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMw1V1LS8NAEB60FdSD1ar4dg8KXqJmt0mzB5H6KC2tQaVCbzHZ3UChtNq0av-Uv9HZPOoD9NaDt8AmC5uZnfm-zGY-gAPOJWehoAbCY2mUhO0bvlC43S0nxFDIAlP6sdhE2XWddpvfzsB79i-MPlaZxcQ4UMu-0N_ITyhHLuIgmHHOn54NrRqlq6uZhEbiFg01fkXKFp3Vr9C-h5RWr1uXNSNVFTAEY2xoyODULzMpQruMWDqwpG0qaZqCarStfSbkzLQ5NaXliDAILZ9y6YuS5gbINiTDeWchX2Il28pB_uLavb2f1C00y4vrqxj7EVs5P5oJIVliNnIySytzf82D39NAnNuqhf_2VpZhKUXRpJK4_QrMqF4RCimiJmm8ioqweDPpShutgpNIWGCyJvqqq95IpTMYkyrm9nj7kWBM3FFSw-qSu5Evk47Ta_AwldWsQ67X76kNIIrZUlEhmKbO6MpByEJuSZzRNh3plzfhOLOjJ9K26lrdo-vF5X3KvIr3zfCbcDR54CnpKPL7rTuZ1b00tETep8m3_h7eh_la66bpNetuYxsWYhmb-KTmDuSGg5HahTnxMuxEg73Uiwk8TttFPgCUsCoR |
| 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=Computing+Complex+Airy+Functions+by+Numerical+Quadrature&rft.jtitle=Numerical+algorithms&rft.au=Gil%2C+Amparo&rft.au=Segura%2C+Javier&rft.au=Temme%2C+Nico+M.&rft.date=2002-05-01&rft.issn=1017-1398&rft.eissn=1572-9265&rft.volume=30&rft.issue=1&rft.spage=11&rft.epage=23&rft_id=info:doi/10.1023%2FA%3A1015636825525&rft.externalDBID=n%2Fa&rft.externalDocID=10_1023_A_1015636825525 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1017-1398&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1017-1398&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1017-1398&client=summon |