{"id":"https://openalex.org/W3023377253","doi":"https://doi.org/10.1023/a:1009936607335","title":"An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation","display_name":"An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation","publication_year":1999,"publication_date":"1999-08-01","ids":{"openalex":"https://openalex.org/W3023377253","doi":"https://doi.org/10.1023/a:1009936607335","mag":"3023377253"},"language":"en","primary_location":{"id":"doi:10.1023/a:1009936607335","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1009936607335","pdf_url":null,"source":{"id":"https://openalex.org/S64721560","display_name":"Reliable Computing","issn_l":"1385-3139","issn":["1385-3139","1573-1340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Reliable Computing","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":"Nedialko S. Nedialkov","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, M5S 3G4","University of Toronto"],"raw_orcid":null,"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":"University of Toronto","institution_ids":["https://openalex.org/I185261750"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002351708","display_name":"Kenneth R. Jackson","orcid":"https://orcid.org/0000-0003-0645-1948"},"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":false,"raw_author_name":"Kenneth R. Jackson","raw_affiliation_strings":["Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, M5S 3G4","University of Toronto"],"raw_orcid":null,"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":"University of Toronto","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":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.38327886,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"5","issue":"3","first_page":"289","last_page":"310"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9997000098228455,"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":0.9997000098228455,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9927999973297119,"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"}},{"id":"https://openalex.org/T11034","display_name":"Digital Filter Design and Implementation","score":0.9656999707221985,"subfield":{"id":"https://openalex.org/subfields/1711","display_name":"Signal Processing"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.7852147817611694},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7799084186553955},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.7438489198684692},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.7379482388496399},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7373903393745422},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7065103054046631},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5996366739273071},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.5889664888381958},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.5079613327980042},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5030028223991394},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4351254999637604},{"id":"https://openalex.org/keywords/interval-arithmetic","display_name":"Interval arithmetic","score":0.4252655804157257},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3037729859352112},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.07302424311637878},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.06662717461585999}],"concepts":[{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.7852147817611694},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7799084186553955},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.7438489198684692},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.7379482388496399},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7373903393745422},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7065103054046631},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5996366739273071},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.5889664888381958},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5079613327980042},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5030028223991394},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4351254999637604},{"id":"https://openalex.org/C191252586","wikidata":"https://www.wikidata.org/wiki/Q1671453","display_name":"Interval arithmetic","level":3,"score":0.4252655804157257},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3037729859352112},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.07302424311637878},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.06662717461585999},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1023/a:1009936607335","is_oa":false,"landing_page_url":"https://doi.org/10.1023/a:1009936607335","pdf_url":null,"source":{"id":"https://openalex.org/S64721560","display_name":"Reliable Computing","issn_l":"1385-3139","issn":["1385-3139","1573-1340"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319965","host_organization_name":"Springer Nature","host_organization_lineage":["https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Reliable Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.35.7195","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.35.7195","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/ned.scan98.ps.Z","raw_type":"text"},{"id":"mag:3023377253","is_oa":false,"landing_page_url":"http://dblp.uni-trier.de/db/conf/scan/scan1998.html#NedialkovJ98","pdf_url":null,"source":{"id":"https://openalex.org/S51527640","display_name":"Scanning","issn_l":"0161-0457","issn":["0161-0457","1932-8745"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"Scanning","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W53809769","https://openalex.org/W57471189","https://openalex.org/W81204410","https://openalex.org/W1589971708","https://openalex.org/W1994309501","https://openalex.org/W2055798134","https://openalex.org/W2076707596","https://openalex.org/W2317827848","https://openalex.org/W4293515545","https://openalex.org/W6601889281"],"related_works":["https://openalex.org/W2147806352","https://openalex.org/W2175862920","https://openalex.org/W1980787211","https://openalex.org/W3137662446","https://openalex.org/W2786196375","https://openalex.org/W3152863516","https://openalex.org/W1984925643","https://openalex.org/W2131944074","https://openalex.org/W185176060","https://openalex.org/W2095455830","https://openalex.org/W3200712362","https://openalex.org/W2971711322","https://openalex.org/W1993693978","https://openalex.org/W3024512247","https://openalex.org/W3197209831","https://openalex.org/W63771258","https://openalex.org/W1985158174","https://openalex.org/W2089448982","https://openalex.org/W2524692928","https://openalex.org/W3106144826"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-19T15:47:20.252518","created_date":"2025-10-10T00:00:00"}
