{"id":"https://openalex.org/W2025630362","doi":"https://doi.org/10.1145/1039813.1039818","title":"Computation of complex Airy functions and their zeros using asymptotics and the differential equation","display_name":"Computation of complex Airy functions and their zeros using asymptotics and the differential equation","publication_year":2004,"publication_date":"2004-12-01","ids":{"openalex":"https://openalex.org/W2025630362","doi":"https://doi.org/10.1145/1039813.1039818","mag":"2025630362"},"language":"en","primary_location":{"id":"doi:10.1145/1039813.1039818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1039813.1039818","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037555548","display_name":"Bruce R. Fabijonas","orcid":null},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"B. R. Fabijonas","raw_affiliation_strings":["Southern Methodist University, Dallas, TX","Southern Methodist University , Dallas , TX"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Southern Methodist University, Dallas, TX","institution_ids":["https://openalex.org/I178169726"]},{"raw_affiliation_string":"Southern Methodist University , Dallas , TX","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082800992","display_name":"Daniel W. Lozier","orcid":null},"institutions":[{"id":"https://openalex.org/I1321296531","display_name":"National Institute of Standards and Technology","ror":"https://ror.org/05xpvk416","country_code":"US","type":"funder","lineage":["https://openalex.org/I1321296531","https://openalex.org/I1343035065"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. W. Lozier","raw_affiliation_strings":["National Institute of Standards and Technology, Gaithersburg, MD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Institute of Standards and Technology, Gaithersburg, MD","institution_ids":["https://openalex.org/I1321296531"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015630594","display_name":"F. W. J. Olver","orcid":null},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"F. W. J. Olver","raw_affiliation_strings":["University of Maryland, College Park, MD"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Maryland, College Park, MD","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.9387,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.73589563,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"30","issue":"4","first_page":"471","last_page":"490"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.984000027179718,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/airy-function","display_name":"Airy function","score":0.8759424686431885},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.7016817331314087},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6606824398040771},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6050652265548706},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.604103147983551},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5445111989974976},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.48195597529411316},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46967536211013794},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.45019060373306274},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.4119725823402405},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.19945019483566284},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14819195866584778},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09507760405540466},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.06924629211425781}],"concepts":[{"id":"https://openalex.org/C140901224","wikidata":"https://www.wikidata.org/wiki/Q409415","display_name":"Airy function","level":2,"score":0.8759424686431885},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.7016817331314087},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6606824398040771},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6050652265548706},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.604103147983551},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5445111989974976},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.48195597529411316},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46967536211013794},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.45019060373306274},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.4119725823402405},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.19945019483566284},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14819195866584778},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09507760405540466},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.06924629211425781},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1145/1039813.1039818","is_oa":false,"landing_page_url":"https://doi.org/10.1145/1039813.1039818","pdf_url":null,"source":{"id":"https://openalex.org/S163326656","display_name":"ACM Transactions on Mathematical Software","issn_l":"0098-3500","issn":["0098-3500","1557-7295"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319798","host_organization_name":"Association for Computing Machinery","host_organization_lineage":["https://openalex.org/P4310319798"],"host_organization_lineage_names":["Association for Computing Machinery"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ACM Transactions on Mathematical Software","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W170420078","https://openalex.org/W1543220654","https://openalex.org/W1549451790","https://openalex.org/W1964366593","https://openalex.org/W1970402433","https://openalex.org/W1973250947","https://openalex.org/W1990695297","https://openalex.org/W1992117405","https://openalex.org/W1994499725","https://openalex.org/W2001450403","https://openalex.org/W2017198186","https://openalex.org/W2017802927","https://openalex.org/W2019895631","https://openalex.org/W2028837575","https://openalex.org/W2042649359","https://openalex.org/W2049884327","https://openalex.org/W2057817591","https://openalex.org/W2075497840","https://openalex.org/W2082546918","https://openalex.org/W2084228668","https://openalex.org/W2096651032","https://openalex.org/W2124601814","https://openalex.org/W2142167905","https://openalex.org/W2170706425","https://openalex.org/W2293275298","https://openalex.org/W2317411137","https://openalex.org/W2503559392","https://openalex.org/W4232362180","https://openalex.org/W4303083268"],"related_works":["https://openalex.org/W2795409807","https://openalex.org/W3099416952","https://openalex.org/W2098174154","https://openalex.org/W2035294016","https://openalex.org/W1964366593","https://openalex.org/W2025630362","https://openalex.org/W137103153","https://openalex.org/W2033024067","https://openalex.org/W1978727346","https://openalex.org/W2020578342"],"abstract_inverted_index":{"We":[0,46],"describe":[1,70],"a":[2],"method":[3],"by":[4],"which":[5],"one":[6],"can":[7],"compute":[8],"the":[9,20,25,35,54,60,65,75,81,88,94],"solutions":[10],"of":[11,34,40,53,80],"Airy's":[12],"differential":[13,36],"equation,":[14],"and":[15,23,38,57,77,84,87,90],"their":[16,85],"derivatives,":[17,86],"both":[18],"on":[19,93],"real":[21,96],"line":[22],"in":[24,50],"complex":[26],"plane.":[27],"The":[28],"computational":[29,67],"methods":[30],"are":[31],"numerical":[32],"integration":[33],"equation":[37],"summation":[39],"asymptotic":[41],"expansions":[42],"for":[43],"large":[44],"argument.":[45],"give":[47],"details":[48],"involved":[49],"obtaining":[51],"all":[52],"parameter":[55],"values,":[56],"we":[58,69],"control":[59],"truncation":[61],"errors":[62],"rigorously.":[63],"Using":[64],"same":[66],"methods,":[68],"an":[71],"algorithm":[72],"that":[73],"computes":[74],"zeros":[76],"associated":[78],"values":[79],"Airy":[82],"functions":[83,92],"modulus":[89],"phase":[91],"negative":[95],"axis.":[97]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
