{"id":"https://openalex.org/W2037007846","doi":"https://doi.org/10.1137/050625837","title":"Optimizing Talbot\u2019s Contours for the Inversion of the Laplace Transform","display_name":"Optimizing Talbot\u2019s Contours for the Inversion of the Laplace Transform","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2037007846","doi":"https://doi.org/10.1137/050625837","mag":"2037007846"},"language":"en","primary_location":{"id":"doi:10.1137/050625837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050625837","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5029496590","display_name":"J. A. C. Weideman","orcid":"https://orcid.org/0000-0002-6833-8222"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. A. C. Weideman","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029496590"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.108,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.97731805,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"44","issue":"6","first_page":"2342","last_page":"2362"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9965999722480774,"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"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9965999722480774,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.994700014591217,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8852722644805908},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7863357067108154},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6118640303611755},{"id":"https://openalex.org/keywords/inversion","display_name":"Inversion (geology)","score":0.5527509450912476},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5154970288276672},{"id":"https://openalex.org/keywords/mellin-transform","display_name":"Mellin transform","score":0.4365770220756531},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.42707839608192444},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4259325861930847},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.3206399083137512}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8852722644805908},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7863357067108154},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6118640303611755},{"id":"https://openalex.org/C1893757","wikidata":"https://www.wikidata.org/wiki/Q3653001","display_name":"Inversion (geology)","level":3,"score":0.5527509450912476},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5154970288276672},{"id":"https://openalex.org/C199874217","wikidata":"https://www.wikidata.org/wiki/Q606934","display_name":"Mellin transform","level":3,"score":0.4365770220756531},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.42707839608192444},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4259325861930847},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.3206399083137512},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C109007969","wikidata":"https://www.wikidata.org/wiki/Q749565","display_name":"Structural basin","level":2,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050625837","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050625837","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:uuid:61b97148-acb9-447f-b42d-3a943153b850","is_oa":false,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1148","raw_type":"Technical Report"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:61b97148-acb9-447f-b42d-3a943153b850","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:61b97148-acb9-447f-b42d-3a943153b850","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://eprints.maths.ox.ac.uk/1148","raw_type":"Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W1490180844","https://openalex.org/W1558122728","https://openalex.org/W1593884873","https://openalex.org/W1602827292","https://openalex.org/W1657347807","https://openalex.org/W1968614732","https://openalex.org/W1981745143","https://openalex.org/W1983001687","https://openalex.org/W1988533746","https://openalex.org/W1994338028","https://openalex.org/W1997924127","https://openalex.org/W2012405708","https://openalex.org/W2022538649","https://openalex.org/W2039099273","https://openalex.org/W2047808645","https://openalex.org/W2051478763","https://openalex.org/W2067136705","https://openalex.org/W2070279765","https://openalex.org/W2106565812","https://openalex.org/W2123426570","https://openalex.org/W2130994331","https://openalex.org/W2135094424","https://openalex.org/W2787959293","https://openalex.org/W2798909945","https://openalex.org/W4252125839"],"related_works":["https://openalex.org/W2786944155","https://openalex.org/W2187664245","https://openalex.org/W3186376410","https://openalex.org/W2152887067","https://openalex.org/W2552456109","https://openalex.org/W2092287764","https://openalex.org/W4387738947","https://openalex.org/W2997260785","https://openalex.org/W2469603162","https://openalex.org/W3022275705"],"abstract_inverted_index":{"Talbot\u2019s":[0],"method":[1,63],"for":[2,42,95],"the":[3,7,14,24,34,40,43,52,54,67,74,79,85,99,105,111,127],"numerical":[4],"inversion":[5],"of":[6,11,23,36,61,76,84,98,107,113,121],"Laplace":[8],"transform":[9],"consists":[10],"numerically":[12],"integrating":[13],"Bromwich":[15],"integral":[16],"on":[17],"a":[18],"special":[19],"contour":[20],"by":[21],"means":[22],"trapezoidal":[25],"or":[26],"midpoint":[27],"rules.":[28],"In":[29,51],"this":[30,62],"paper":[31],"we":[32],"address":[33],"issue":[35],"parameter":[37],"selection":[38],"in":[39,78],"method,":[41],"particular":[44],"situation":[45],"when":[46],"parabolic":[47],"PDEs":[48],"are":[49,102],"solved.":[50],"process":[53],"well\u2010known":[55],"subgeometric":[56],"convergence":[57],"rate":[58,69,88],"$O(\\exp(-c":[59,70],"\\sqrt{N}))$":[60],"is":[64,90,115],"improved":[65],"to":[66,117,132],"geometric":[68],"N))$,":[71],"with":[72],"N":[73],"number":[75],"nodes":[77],"integration":[80],"rule.":[81],"The":[82],"value":[83],"maximum":[86],"decay":[87],"c":[89],"explicitly":[91],"determined.":[92],"Numerical":[93],"results":[94],"two":[96],"versions":[97],"heat":[100],"equation":[101],"presented.":[103],"With":[104],"choice":[106],"parameters":[108],"derived":[109],"here,":[110],"rule":[112],"thumb":[114],"that":[116],"achieve":[118],"an":[119],"accuracy":[120],"$10^{-\\ell}$":[122],"at":[123],"any":[124],"given":[125],"time,":[126],"associated":[128],"elliptic":[129],"problem":[130],"has":[131],"be":[133],"solved":[134],"no":[135],"more":[136],"than":[137],"$\\ell$":[138],"times.":[139]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":6}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}