{"id":"https://openalex.org/W2012580470","doi":"https://doi.org/10.1016/s0096-3003(98)10083-8","title":"Validated solutions of initial value problems for ordinary differential equations","display_name":"Validated solutions of initial value problems for ordinary differential equations","publication_year":1999,"publication_date":"1999-10-01","ids":{"openalex":"https://openalex.org/W2012580470","doi":"https://doi.org/10.1016/s0096-3003(98)10083-8","mag":"2012580470"},"language":"en","primary_location":{"id":"doi:10.1016/s0096-3003(98)10083-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(98)10083-8","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","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/A5006886777","display_name":"Nedialko S. Nedialkov","orcid":"https://orcid.org/0000-0001-8697-4428"},"institutions":[{"id":"https://openalex.org/I185261750","display_name":"University of Toronto","ror":"https://ror.org/03dbr7087","country_code":"CA","type":"education","lineage":["https://openalex.org/I185261750"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"N Nedialkov","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4","Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4","institution_ids":["https://openalex.org/I185261750"]},{"raw_affiliation_string":"Department of Computer Science, University of Toronto, Toronto, Ontario, Canada M5S 3G4#TAB#","institution_ids":["https://openalex.org/I185261750"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5006886777"],"corresponding_institution_ids":["https://openalex.org/I185261750"],"apc_list":{"value":3550,"currency":"USD","value_usd":3550},"apc_paid":null,"fwci":8.3041,"has_fulltext":false,"cited_by_count":359,"citation_normalized_percentile":{"value":0.97966963,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"105","issue":"1","first_page":"21","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9934999942779541,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.8564184904098511},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.8434766530990601},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.8121181726455688},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5387618541717529},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.511062502861023},{"id":"https://openalex.org/keywords/enclosure","display_name":"Enclosure","score":0.48072412610054016},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38755157589912415},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38286834955215454},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29390910267829895}],"concepts":[{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.8564184904098511},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.8434766530990601},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.8121181726455688},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5387618541717529},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.511062502861023},{"id":"https://openalex.org/C98375054","wikidata":"https://www.wikidata.org/wiki/Q442709","display_name":"Enclosure","level":2,"score":0.48072412610054016},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38755157589912415},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38286834955215454},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29390910267829895},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/s0096-3003(98)10083-8","is_oa":false,"landing_page_url":"https://doi.org/10.1016/s0096-3003(98)10083-8","pdf_url":null,"source":{"id":"https://openalex.org/S50372074","display_name":"Applied Mathematics and Computation","issn_l":"0096-3003","issn":["0096-3003","1873-5649"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Applied Mathematics and Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.34.7825","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.34.7825","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.toronto.edu/pub/reports/na/vsode.97.ps.Z","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W57471189","https://openalex.org/W75673531","https://openalex.org/W174370412","https://openalex.org/W999733437","https://openalex.org/W1483874187","https://openalex.org/W1489214402","https://openalex.org/W1531587267","https://openalex.org/W1539736615","https://openalex.org/W1560553581","https://openalex.org/W1574435983","https://openalex.org/W1588000771","https://openalex.org/W1965941849","https://openalex.org/W1975761579","https://openalex.org/W1997762249","https://openalex.org/W2001805159","https://openalex.org/W2060924166","https://openalex.org/W2065783629","https://openalex.org/W2071157109","https://openalex.org/W2084483425","https://openalex.org/W2086900155","https://openalex.org/W2093178179","https://openalex.org/W2094389332","https://openalex.org/W3185484028","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W3082668976","https://openalex.org/W2517973022","https://openalex.org/W1543121148","https://openalex.org/W1580703421","https://openalex.org/W2996841952","https://openalex.org/W2618518959","https://openalex.org/W2231364979","https://openalex.org/W4295745414","https://openalex.org/W4288093367","https://openalex.org/W2059261580"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":21},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":20},{"year":2015,"cited_by_count":23},{"year":2014,"cited_by_count":17},{"year":2013,"cited_by_count":14},{"year":2012,"cited_by_count":21}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
