{"id":"https://openalex.org/W368699053","doi":"https://doi.org/10.1155/2011/582740","title":"The Exponential Dichotomy under Discretization on General Approximation Scheme","display_name":"The Exponential Dichotomy under Discretization on General Approximation Scheme","publication_year":2011,"publication_date":"2011-02-14","ids":{"openalex":"https://openalex.org/W368699053","doi":"https://doi.org/10.1155/2011/582740","mag":"368699053"},"language":"en","primary_location":{"id":"doi:10.1155/2011/582740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2011/582740","pdf_url":"https://downloads.hindawi.com/archive/2011/582740.pdf","source":{"id":"https://openalex.org/S120697665","display_name":"Advances in Numerical Analysis","issn_l":"1687-9562","issn":["1687-9562","1687-9570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/archive/2011/582740.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025442717","display_name":"Javier Pastor","orcid":null},"institutions":[{"id":"https://openalex.org/I16097986","display_name":"Universitat de Val\u00e8ncia","ror":"https://ror.org/043nxc105","country_code":"ES","type":"education","lineage":["https://openalex.org/I16097986"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Javier Pastor","raw_affiliation_strings":["Department de Mathem\u00e0tica Aplicada, University de Val\u00e8ncia, 46100 Burjassot, Valencia, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department de Mathem\u00e0tica Aplicada, University de Val\u00e8ncia, 46100 Burjassot, Valencia, Spain","institution_ids":["https://openalex.org/I16097986"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015416833","display_name":"Sergey Piskarev","orcid":"https://orcid.org/0000-0002-2487-6870"},"institutions":[{"id":"https://openalex.org/I19880235","display_name":"Lomonosov Moscow State University","ror":"https://ror.org/010pmpe69","country_code":"RU","type":"education","lineage":["https://openalex.org/I19880235"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Sergey Piskarev","raw_affiliation_strings":["Scientific Research Computer Center, Moscow State University, Vorobjevy Gory, Moscow 119899, Russia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Scientific Research Computer Center, Moscow State University, Vorobjevy Gory, Moscow 119899, Russia","institution_ids":["https://openalex.org/I19880235"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5025442717"],"corresponding_institution_ids":["https://openalex.org/I16097986"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.02560792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2011","issue":"5","first_page":"1","last_page":"22"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991000294685364,"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":0.9990000128746033,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8048471212387085},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.71739661693573},{"id":"https://openalex.org/keywords/exponential-dichotomy","display_name":"Exponential dichotomy","score":0.5244783759117126},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5137683153152466},{"id":"https://openalex.org/keywords/generator","display_name":"Generator (circuit theory)","score":0.5044642686843872},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4977848529815674},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44469523429870605},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4365460276603699},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.41005152463912964},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09205502271652222},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.0879749059677124},{"id":"https://openalex.org/keywords/power","display_name":"Power (physics)","score":0.07922044396400452}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8048471212387085},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.71739661693573},{"id":"https://openalex.org/C2779844894","wikidata":"https://www.wikidata.org/wiki/Q5421516","display_name":"Exponential dichotomy","level":3,"score":0.5244783759117126},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5137683153152466},{"id":"https://openalex.org/C2780992000","wikidata":"https://www.wikidata.org/wiki/Q17016113","display_name":"Generator (circuit theory)","level":3,"score":0.5044642686843872},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4977848529815674},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44469523429870605},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4365460276603699},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.41005152463912964},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09205502271652222},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0879749059677124},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.07922044396400452},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","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/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2011/582740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2011/582740","pdf_url":"https://downloads.hindawi.com/archive/2011/582740.pdf","source":{"id":"https://openalex.org/S120697665","display_name":"Advances in Numerical Analysis","issn_l":"1687-9562","issn":["1687-9562","1687-9570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:hindawi.com:10.1155/2011/582740","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2011/582740","pdf_url":null,"source":{"id":"https://openalex.org/S4306400340","display_name":"Hindawi Journal of Chemistry (Hindawi)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210126990","host_organization_name":"Hindawi (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210126990"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Research Article"},{"id":"mag:368699053","is_oa":false,"landing_page_url":"http://istina.msu.ru/publications/article/3535045/","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"doi:10.1155/2011/582740","is_oa":true,"landing_page_url":"http://doi.org/10.1155/2011/582740","pdf_url":"https://downloads.hindawi.com/archive/2011/582740.pdf","source":{"id":"https://openalex.org/S120697665","display_name":"Advances in Numerical Analysis","issn_l":"1687-9562","issn":["1687-9562","1687-9570"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869"],"host_organization_lineage_names":["Hindawi Publishing Corporation"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Numerical Analysis","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.41999998688697815,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G4051603784","display_name":null,"funder_award_id":"SFB 701","funder_id":"https://openalex.org/F4320323389","funder_display_name":"Universit\u00e4t Bielefeld"}],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"},{"id":"https://openalex.org/F4320321851","display_name":"Fudan University","ror":"https://ror.org/013q1eq08"},{"id":"https://openalex.org/F4320323389","display_name":"Universit\u00e4t Bielefeld","ror":"https://ror.org/02hpadn98"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W368699053.pdf","grobid_xml":"https://content.openalex.org/works/W368699053.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W181691505","https://openalex.org/W187422796","https://openalex.org/W621351040","https://openalex.org/W1529663478","https://openalex.org/W1537906002","https://openalex.org/W1560060148","https://openalex.org/W1965532925","https://openalex.org/W1971896291","https://openalex.org/W1986595153","https://openalex.org/W2000436005","https://openalex.org/W2026362836","https://openalex.org/W2081817996","https://openalex.org/W2083283896","https://openalex.org/W2106070738","https://openalex.org/W2108503476","https://openalex.org/W2117137514","https://openalex.org/W2130253263","https://openalex.org/W2324420703","https://openalex.org/W2333576939","https://openalex.org/W3152504699"],"related_works":["https://openalex.org/W2133274234","https://openalex.org/W3016749842","https://openalex.org/W3145468792","https://openalex.org/W2963535445","https://openalex.org/W2016383951","https://openalex.org/W3112705464","https://openalex.org/W2963834145","https://openalex.org/W3026935255","https://openalex.org/W2615866445","https://openalex.org/W2021856295","https://openalex.org/W2100511085","https://openalex.org/W3109684313","https://openalex.org/W2289548509","https://openalex.org/W2952864205","https://openalex.org/W2951382126","https://openalex.org/W2883299057","https://openalex.org/W1997345083","https://openalex.org/W2104082587","https://openalex.org/W2463117017","https://openalex.org/W3211578012"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,44,72,119],"devoted":[3],"to":[4,24,74,98],"the":[5,49,53,56,67,88,105],"numerical":[6],"analysis":[7],"of":[8,36,55,90,104,116],"abstract":[9],"parabolic":[10],"problem":[11,71],";":[12],",":[13],"with":[14,78,126],"hyperbolic":[15,57],"generator":[16],".":[17],"We":[18,86],"are":[19],"developing":[20],"a":[21,26,30,45,63,102],"general":[22,32,110],"approach":[23],"establish":[25],"discrete":[27,37],"dichotomy":[28],"in":[29,34,39,52,62,82,122],"very":[31],"setting":[33],"case":[35],"approximation":[38,92,97,111],"space":[40,51],"and":[41,94,129,132],"time.":[42],"It":[43],"well-known":[46],"fact":[47],"that":[48,66,100],"phase":[50],"neighborhood":[54],"equilibrium":[58],"can":[59,133],"be":[60,134],"split":[61],"such":[64,101],"way":[65],"original":[68],"initial":[69,75],"value":[70,76],"reduced":[73],"problems":[77],"exponential":[79],"decaying":[80],"solutions":[81],"opposite":[83],"time":[84],"direction.":[85],"use":[87],"theory":[89],"compact":[91,127],"principle":[93],"collectively":[95],"condensing":[96,130],"show":[99],"decomposition":[103],"flow":[106],"persists":[107],"under":[108],"rather":[109],"schemes.":[112],"The":[113],"main":[114],"assumption":[115],"our":[117],"results":[118],"naturally":[120],"satisfied,":[121],"particular,":[123],"for":[124,136],"operators":[125],"resolvents":[128],"semigroups":[131],"verified":[135],"finite":[137,142],"element":[138],"as":[139,141],"well":[140],"difference":[143],"methods.":[144]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
