{"id":"https://openalex.org/W2025733636","doi":"https://doi.org/10.1137/040604388","title":"Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations","display_name":"Bounding the Solutions of Parameter Dependent Nonlinear Ordinary Differential Equations","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2025733636","doi":"https://doi.org/10.1137/040604388","mag":"2025733636"},"language":"en","primary_location":{"id":"doi:10.1137/040604388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040604388","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific 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/A5082263078","display_name":"Adam B. Singer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adam B. Singer","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5037278011","display_name":"Paul I. Barton","orcid":"https://orcid.org/0000-0003-2895-9443"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul I. Barton","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.9475,"has_fulltext":false,"cited_by_count":88,"citation_normalized_percentile":{"value":0.98284994,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"27","issue":"6","first_page":"2167","last_page":"2182"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9994999766349792,"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/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11236","display_name":"Control Systems and Identification","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8125646710395813},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.7713760733604431},{"id":"https://openalex.org/keywords/bounding-overwatch","display_name":"Bounding overwatch","score":0.623991072177887},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5791252255439758},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5683273673057556},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.5374377965927124},{"id":"https://openalex.org/keywords/euclidean-space","display_name":"Euclidean space","score":0.4790721833705902},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.44688764214515686},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44478827714920044},{"id":"https://openalex.org/keywords/distributed-parameter-system","display_name":"Distributed parameter system","score":0.4272419810295105},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.418844997882843},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4127132296562195},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3875746726989746},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1391819715499878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8125646710395813},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.7713760733604431},{"id":"https://openalex.org/C63584917","wikidata":"https://www.wikidata.org/wiki/Q333286","display_name":"Bounding overwatch","level":2,"score":0.623991072177887},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5791252255439758},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5683273673057556},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.5374377965927124},{"id":"https://openalex.org/C186450821","wikidata":"https://www.wikidata.org/wiki/Q17295","display_name":"Euclidean space","level":2,"score":0.4790721833705902},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.44688764214515686},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44478827714920044},{"id":"https://openalex.org/C112714845","wikidata":"https://www.wikidata.org/wiki/Q1482001","display_name":"Distributed parameter system","level":3,"score":0.4272419810295105},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.418844997882843},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4127132296562195},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3875746726989746},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1391819715499878},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/040604388","is_oa":false,"landing_page_url":"https://doi.org/10.1137/040604388","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":10,"referenced_works":["https://openalex.org/W1488416636","https://openalex.org/W1574435983","https://openalex.org/W1580809199","https://openalex.org/W1585773866","https://openalex.org/W1972629843","https://openalex.org/W1984064362","https://openalex.org/W1988622494","https://openalex.org/W2018431647","https://openalex.org/W2069325543","https://openalex.org/W4302562054"],"related_works":["https://openalex.org/W2006263304","https://openalex.org/W2155548976","https://openalex.org/W2496629542","https://openalex.org/W2063772434","https://openalex.org/W3020098708","https://openalex.org/W2482000553","https://openalex.org/W4292934066","https://openalex.org/W4320000798","https://openalex.org/W623644139","https://openalex.org/W3195236465"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"two":[3],"techniques":[4],"for":[5,55],"generating":[6],"rigorous":[7],"bounds":[8,37],"on":[9,78],"the":[10,30,43,46,65,68,90,93,109],"solution":[11,44,69],"of":[12,25,32,42,45,64,67,70,73,80,92,101],"parameter":[13,74],"dependent":[14,75],"nonlinear":[15],"ordinary":[16],"differential":[17,26,47,76],"equations.":[18,48],"The":[19,49,95],"first":[20],"technique":[21,51],"is":[22],"an":[23],"extension":[24],"inequalities":[27],"that":[28],"enables":[29],"construction":[31,91],"tight":[33],"time":[34,59],"varying":[35],"state":[36],"by":[38],"utilizing":[39],"prior":[40],"knowledge":[41],"second":[50],"provides":[52],"a":[53,71,81,98,102],"method":[54],"constructing":[56],"pointwise":[57],"in":[58],"convex":[60],"and":[61],"concave":[62],"relaxations":[63],"image":[66],"system":[72],"equations":[77],"subsets":[79],"Euclidean":[82],"space.":[83],"Two":[84],"examples":[85,96],"are":[86],"presented":[87],"to":[88,106],"demonstrate":[89],"bounds.":[94,110],"include":[97],"brief":[99],"discussion":[100],"computer":[103],"program":[104],"written":[105],"automatically":[107],"generate":[108]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":8}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}