{"id":"https://openalex.org/W2139670194","doi":"https://doi.org/10.1137/s1064827502409717","title":"An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays","display_name":"An Analysis of Delay-Dependent Stability for Ordinary and Partial Differential Equations with Fixed and Distributed Delays","publication_year":2004,"publication_date":"2004-01-01","ids":{"openalex":"https://openalex.org/W2139670194","doi":"https://doi.org/10.1137/s1064827502409717","mag":"2139670194"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827502409717","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502409717","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":true,"oa_status":"green","oa_url":"http://gateway.newisiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=CCC&SrcApp=PRODUCT_NAME&SrcURL=WOS_RETURN_URL&CKEY=HUAN1608040025SC&DestLinkType=FullRecord&DestApp=CCC&SrcDesc=RETURN_ALT_TEXT&SrcAppSID=APP_SID","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100651262","display_name":"Chengming Huang","orcid":"https://orcid.org/0000-0001-8556-1111"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Chengming Huang","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B3001 Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Stefan Vandewalle","raw_affiliation_strings":["Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B3001 Leuven, Belgium"],"affiliations":[{"raw_affiliation_string":"Katholieke Universiteit Leuven, Department of Computer Science, Celestijnenlaan 200A, B3001 Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100651262"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":null,"apc_paid":null,"fwci":3.5087,"has_fulltext":false,"cited_by_count":92,"citation_normalized_percentile":{"value":0.92400744,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"25","issue":"5","first_page":"1608","last_page":"1632"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T11416","display_name":"Numerical methods for differential equations","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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9991999864578247,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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/mathematics","display_name":"Mathematics","score":0.8484504222869873},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.7133329510688782},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6571422815322876},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6487006545066833},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6417986750602722},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5447796583175659},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.49634724855422974},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.46268051862716675},{"id":"https://openalex.org/keywords/stochastic-partial-differential-equation","display_name":"Stochastic partial differential equation","score":0.4484991729259491},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.43930286169052124},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4293793737888336},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4207780957221985},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3613467216491699},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.2708025574684143},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07153183221817017},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06906789541244507}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8484504222869873},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.7133329510688782},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6571422815322876},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6487006545066833},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6417986750602722},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5447796583175659},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.49634724855422974},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.46268051862716675},{"id":"https://openalex.org/C84629840","wikidata":"https://www.wikidata.org/wiki/Q16979017","display_name":"Stochastic partial differential equation","level":3,"score":0.4484991729259491},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.43930286169052124},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4293793737888336},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4207780957221985},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3613467216491699},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2708025574684143},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07153183221817017},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06906789541244507},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827502409717","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827502409717","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"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/123828","is_oa":true,"landing_page_url":"http://gateway.newisiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=CCC&SrcApp=PRODUCT_NAME&SrcURL=WOS_RETURN_URL&CKEY=HUAN1608040025SC&DestLinkType=FullRecord&DestApp=CCC&SrcDesc=RETURN_ALT_TEXT&SrcAppSID=APP_SID","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol. 25 (5), Art.No. 5, (1608-1632)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/123828","is_oa":true,"landing_page_url":"http://gateway.newisiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=CCC&SrcApp=PRODUCT_NAME&SrcURL=WOS_RETURN_URL&CKEY=HUAN1608040025SC&DestLinkType=FullRecord&DestApp=CCC&SrcDesc=RETURN_ALT_TEXT&SrcAppSID=APP_SID","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol. 25 (5), Art.No. 5, (1608-1632)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W40822717","https://openalex.org/W1550341792","https://openalex.org/W1605753492","https://openalex.org/W1937028141","https://openalex.org/W1970448574","https://openalex.org/W1976771036","https://openalex.org/W1978082100","https://openalex.org/W1980654598","https://openalex.org/W2005775749","https://openalex.org/W2019317114","https://openalex.org/W2027407479","https://openalex.org/W2028331352","https://openalex.org/W2049502525","https://openalex.org/W2061921867","https://openalex.org/W2062346768","https://openalex.org/W2068573901","https://openalex.org/W2079708759","https://openalex.org/W2085620203","https://openalex.org/W2090445374","https://openalex.org/W2347101115","https://openalex.org/W2524994179","https://openalex.org/W2799664482"],"related_works":["https://openalex.org/W2088064134","https://openalex.org/W2009573643","https://openalex.org/W2066872858","https://openalex.org/W2593379477","https://openalex.org/W2044958912","https://openalex.org/W2126272980","https://openalex.org/W3000107235","https://openalex.org/W4200582678","https://openalex.org/W2093617977","https://openalex.org/W2139670194"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,72,116,124,127,148,171],"concerned":[3],"with":[4,16,23,37,48],"the":[5,8,24,27,53,58,65,68,80,85,89,96,100,112,130,138,142,152,158,162,167],"study":[6,25,52,103],"of":[7,10,26,29,31,43,57,64,67,92,99,111,137,161],"stability":[9,28,41,55,87,109,139,160],"ordinary":[11,45],"and":[12,19,22,176,182],"partial":[13,105,168],"differential":[14,33,46,106,169],"equations":[15,47],"both":[17,173],"fixed":[18],"distributed":[20],"delays,":[21],"discretizations":[30],"such":[32],"equations.":[34,107],"We":[35,51],"start":[36],"a":[38,62,75,120,135],"delay-dependent":[39,159],"asymptotic":[40,86],"analysis":[42],"scalar":[44],"real":[49],"coefficients.":[50],"exact":[54],"region":[56,110,140],"continuous":[59,114],"problem":[60,115],"as":[61],"function":[63],"parameters":[66],"model.":[69],"Next,":[70],"it":[71],"proved":[73],"that":[74,129],"time":[76],"discretization":[77,132],"based":[78],"on":[79],"trapezium":[81],"rule":[82],"can":[83],"preserve":[84],"for":[88],"considered":[90],"set":[91],"test":[93],"problems.":[94],"In":[95],"second":[97],"part":[98],"paper,":[101],"we":[102,156],"delay":[104],"The":[108],"fully":[113,163],"analyzed":[117],"first.":[118],"Then":[119],"semidiscretization":[121],"in":[122,174,177],"space":[123,175],"applied.":[125],"It":[126],"shown":[128],"spatial":[131],"leads":[133],"to":[134,150],"reduction":[136],"when":[141],"standard":[143],"second-order":[144],"central":[145],"difference":[146],"operator":[147],"employed":[149],"approximate":[151],"diffusion":[153],"operator.":[154],"Finally":[155],"consider":[157],"discrete":[164],"problem,":[165],"where":[166],"equation":[170],"discretized":[172],"time.":[178],"Some":[179],"numerical":[180],"examples":[181],"further":[183],"discussions":[184],"are":[185],"given.":[186]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":12},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
