{"id":"https://openalex.org/W2022358579","doi":"https://doi.org/10.1137/060654116","title":"Stability Analysis of $\\Theta$-Methods for Nonlinear Neutral Functional Differential Equations","display_name":"Stability Analysis of $\\Theta$-Methods for Nonlinear Neutral Functional Differential Equations","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2022358579","doi":"https://doi.org/10.1137/060654116","mag":"2022358579"},"language":"en","primary_location":{"id":"doi:10.1137/060654116","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654116","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/A5014198183","display_name":"Wansheng Wang","orcid":"https://orcid.org/0000-0002-2128-7501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wansheng Wang","raw_affiliation_strings":["w.s.wang@163.com#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"w.s.wang@163.com#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009101042","display_name":"Shoufu Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shoufu Li","raw_affiliation_strings":["[email\u00a0protected]#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"[email\u00a0protected]#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0387,"has_fulltext":false,"cited_by_count":31,"citation_normalized_percentile":{"value":0.90480528,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"30","issue":"4","first_page":"2181","last_page":"2205"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9945999979972839,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.8594282865524292},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6661920547485352},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5973213911056519},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5967714786529541},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5828701853752136},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.5744278430938721},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5353890657424927},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5257304906845093},{"id":"https://openalex.org/keywords/stability-theory","display_name":"Stability theory","score":0.49996376037597656},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4292120933532715},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.39777621626853943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3799477815628052},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08884137868881226}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8594282865524292},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6661920547485352},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5973213911056519},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5967714786529541},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5828701853752136},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.5744278430938721},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5353890657424927},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5257304906845093},{"id":"https://openalex.org/C41949839","wikidata":"https://www.wikidata.org/wiki/Q1756677","display_name":"Stability theory","level":3,"score":0.49996376037597656},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4292120933532715},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.39777621626853943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3799477815628052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08884137868881226},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060654116","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060654116","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":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W29277913","https://openalex.org/W1968898746","https://openalex.org/W1969409177","https://openalex.org/W1977799555","https://openalex.org/W1991877218","https://openalex.org/W1992147499","https://openalex.org/W1993179496","https://openalex.org/W1995021376","https://openalex.org/W2005238669","https://openalex.org/W2007212397","https://openalex.org/W2007716695","https://openalex.org/W2017595816","https://openalex.org/W2035460619","https://openalex.org/W2095151500","https://openalex.org/W2128358316","https://openalex.org/W2169303215","https://openalex.org/W2169378796","https://openalex.org/W2409760985"],"related_works":["https://openalex.org/W4388482258","https://openalex.org/W2963352210","https://openalex.org/W2131431484","https://openalex.org/W2102789413","https://openalex.org/W1708834020","https://openalex.org/W4301805170","https://openalex.org/W2096467061","https://openalex.org/W1532287630","https://openalex.org/W2940603871","https://openalex.org/W2052500721"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,32,47,75,88,100,115,136,139,146,159,163,171],"numerical":[4,35,48,160],"solutions":[5,36,161],"of":[6,21,34,74,138],"nonlinear":[7],"neutral":[8,22,51,79,94,164],"differential":[9,24,52,80],"equations":[10,53,81,95],"with":[11,15,54,82,96,166],"constant":[12,55,97],"delay":[13,56,98,168],"and":[14,60,71,99,177],"proportional":[16,83,167],"delay,":[17,84],"two":[18,85,143,172],"typical":[19],"examples":[20],"functional":[23],"equations,":[25],"are":[26,67,110,174],"investigated.":[27,131],"The":[28,112],"focus":[29],"is":[30,41,57,129,152],"on":[31,107,114,148],"stability":[33,70,73],"produced":[37,169],"by":[38,170],"$\\theta$-methods.":[39],"It":[40,151],"proved":[42,154],"that":[43,155],"if":[44,180],"$\\frac{1}{2}\\leq\\theta\\leq":[45],"1$":[46],"solution":[49],"to":[50,90,102,123,162],"globally":[58,175],"stable":[59,62,176,179],"asymptotically":[61,178],"under":[63,156],"some":[64,157],"conditions":[65],"which":[66,121],"sufficient":[68],"for":[69,126,145],"asymptotic":[72],"exact":[76],"solution.":[77],"For":[78],"discretization":[86],"approaches,":[87,128],"approach":[89,101],"transforming":[91],"it":[92,105],"into":[93,134],"directly":[103],"discretizing":[104],"based":[106],"full-geometric":[108],"mesh,":[109],"discussed.":[111],"integration":[113,147],"first":[116],"mesh":[117],"interval":[118],"$[0,":[119,149],"T_0]$,":[120],"needs":[122],"be":[124],"considered":[125],"both":[127],"also":[130,153],"By":[132],"taking":[133],"account":[135],"order":[137],"methods,":[140],"we":[141],"construct":[142],"algorithms":[144],"T_0]$.":[150],"assumptions":[158],"equation":[165],"approaches":[173],"$\\frac{1}{2}":[181],"<":[182],"\\theta\\leq":[183],"1$.":[184]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}