{"id":"https://openalex.org/W2090767497","doi":"https://doi.org/10.1137/s003614299935591x","title":"On Error Estimates for Waveform Relaxation Methods for Delay-Differential Equations","display_name":"On Error Estimates for Waveform Relaxation Methods for Delay-Differential Equations","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2090767497","doi":"https://doi.org/10.1137/s003614299935591x","mag":"2090767497"},"language":"en","primary_location":{"id":"doi:10.1137/s003614299935591x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614299935591x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5079890441","display_name":"Z. Bartoszewski","orcid":"https://orcid.org/0000-0002-2505-473X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Z. Bartoszewski","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5011090517","display_name":"M. Kwapisz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Kwapisz","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5079890441"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.21030195,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"38","issue":"2","first_page":"639","last_page":"659"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9966999888420105,"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":0.9966999888420105,"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":0.9918000102043152,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9695000052452087,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7981044054031372},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.784009575843811},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.760127067565918},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.6688024997711182},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.5851393342018127},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5151883363723755},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5027389526367188},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34501779079437256},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11886107921600342}],"concepts":[{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7981044054031372},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.784009575843811},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760127067565918},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.6688024997711182},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.5851393342018127},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5151883363723755},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5027389526367188},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34501779079437256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11886107921600342},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C554190296","wikidata":"https://www.wikidata.org/wiki/Q47528","display_name":"Radar","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s003614299935591x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s003614299935591x","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300010721/15","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010721/15&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"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":13,"referenced_works":["https://openalex.org/W192797472","https://openalex.org/W1509997287","https://openalex.org/W1980309222","https://openalex.org/W2005433132","https://openalex.org/W2023344463","https://openalex.org/W2062346768","https://openalex.org/W2081745365","https://openalex.org/W2085385512","https://openalex.org/W2094071032","https://openalex.org/W2104473640","https://openalex.org/W3209416867","https://openalex.org/W4213104200","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2163370649","https://openalex.org/W1261320338","https://openalex.org/W1675687971","https://openalex.org/W2942981489","https://openalex.org/W2924035449","https://openalex.org/W2954452568","https://openalex.org/W4226042226","https://openalex.org/W2086307616","https://openalex.org/W2903509708","https://openalex.org/W4388044483"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,26,34,39,51,62,70,78,82,93,106,113,118,122,135,138],"problem":[4],"of":[5,16,41,81,103,105,125,140],"delay-dependent":[6],"error":[7,35,53,63],"estimates":[8,36,47,54,64,137],"for":[9,55,127],"waveform":[10,114],"relaxation":[11,56,115],"methods":[12,116],"applied":[13],"to":[14,60],"systems":[15],"delay-differential":[17,129],"equations":[18,130],"is":[19,31,86],"discussed.":[20],"Under":[21],"suitable":[22],"conditions":[23],"imposed":[24],"on":[25,38],"so-called":[27],"splitting":[28],"function":[29],"it":[30],"shown":[32],"how":[33,44],"depend":[37],"character":[40],"delays":[42],"and":[43],"much":[45],"these":[46,141],"are":[48],"better":[49],"than":[50],"known":[52],"methods.":[57],"We":[58],"attempt":[59],"derive":[61],"as":[65,67,121],"sharp":[66],"possible":[68],"under":[69,90],"assumed":[71],"conditions.":[72],"Our":[73],"approach":[74],"takes":[75],"into":[76],"account":[77],"specific":[79],"properties":[80],"considered":[83],"equations.":[84],"It":[85],"also":[87],"proved":[88],"that":[89,112],"some":[91],"assumptions":[92],"exact":[94],"solution":[95],"can":[96,143],"be":[97,144],"obtained":[98],"after":[99],"a":[100],"finite":[101],"number":[102,139],"steps":[104,126,142],"iterative":[107],"process;":[108],"i.e.,":[109],"we":[110],"prove":[111],"have":[117],"same":[119],"property":[120],"classical":[123],"method":[124],"solving":[128],"with":[131],"nonvanishing":[132],"delays.":[133],"From":[134],"given":[136],"found.":[145]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}