{"id":"https://openalex.org/W1661172117","doi":"https://doi.org/10.1023/a:1019169114976","title":"Probabilistic and deterministic convergence proofs for software for initial value problems","display_name":"Probabilistic and deterministic convergence proofs for software for initial value problems","publication_year":1997,"publication_date":"1997-04-01","ids":{"openalex":"https://openalex.org/W1661172117","doi":"https://doi.org/10.1023/a:1019169114976","mag":"1661172117"},"language":"en","primary_location":{"id":"doi:10.1023/a:1019169114976","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1019169114976","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5032114852","display_name":"Andrew M. Stuart","orcid":"https://orcid.org/0000-0001-9091-7266"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]},{"id":"https://openalex.org/I4210138427","display_name":"Computational Physics (United States)","ror":"https://ror.org/03grsxg62","country_code":"US","type":"company","lineage":["https://openalex.org/I4210138427"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. M. Stuart","raw_affiliation_strings":["Scientific Computing and Computational Mathematics Program, Division of Mechanics and Computation, Stanford University, Durand 257, Stanford, CA, 94305-4040, USA","Scientific Computing and Computational Mathematics Program Division of Mechanics and Computation, Stanford University, Stanford, USA"],"affiliations":[{"raw_affiliation_string":"Scientific Computing and Computational Mathematics Program, Division of Mechanics and Computation, Stanford University, Durand 257, Stanford, CA, 94305-4040, USA","institution_ids":["https://openalex.org/I4210138427","https://openalex.org/I97018004"]},{"raw_affiliation_string":"Scientific Computing and Computational Mathematics Program Division of Mechanics and Computation, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I4210138427","https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5032114852"],"corresponding_institution_ids":["https://openalex.org/I4210138427","https://openalex.org/I97018004"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":3.2501,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.92440318,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"14","issue":"1-3","first_page":"227","last_page":"260"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9660000205039978,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9660000205039978,"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/theory-of-computation","display_name":"Theory of computation","score":0.7173582911491394},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.674538254737854},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5734813213348389},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.5661708116531372},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5508777499198914},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5236565470695496},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47308188676834106},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.45464643836021423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44663873314857483},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43399035930633545},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.41704657673835754},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.41539669036865234},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.13337093591690063}],"concepts":[{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.7173582911491394},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.674538254737854},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5734813213348389},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5661708116531372},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5508777499198914},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5236565470695496},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47308188676834106},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.45464643836021423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44663873314857483},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43399035930633545},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.41704657673835754},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.41539669036865234},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.13337093591690063},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1023/a:1019169114976","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1019169114976","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:authors.library.caltech.edu:78168","is_oa":false,"landing_page_url":"https://authors.library.caltech.edu/78168/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320309321","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1535429593","https://openalex.org/W2012062489","https://openalex.org/W2048204362","https://openalex.org/W2048903381","https://openalex.org/W2067819709","https://openalex.org/W2088953326","https://openalex.org/W2089057240","https://openalex.org/W2102340303","https://openalex.org/W2115780241","https://openalex.org/W2130331538","https://openalex.org/W2133428703","https://openalex.org/W2144493917","https://openalex.org/W2167097994","https://openalex.org/W2981569720","https://openalex.org/W4232500778"],"related_works":["https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2162899405","https://openalex.org/W2044987316","https://openalex.org/W2237480245","https://openalex.org/W3134374554","https://openalex.org/W2519167559","https://openalex.org/W2075065631","https://openalex.org/W4288358396","https://openalex.org/W4311248832"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
