{"id":"https://openalex.org/W4379983453","doi":"https://doi.org/10.1007/s10208-023-09614-x","title":"High-Order Lohner-Type Algorithm for Rigorous Computation of Poincar\u00e9 Maps in Systems of Delay Differential Equations with Several Delays","display_name":"High-Order Lohner-Type Algorithm for Rigorous Computation of Poincar\u00e9 Maps in Systems of Delay Differential Equations with Several Delays","publication_year":2023,"publication_date":"2023-06-09","ids":{"openalex":"https://openalex.org/W4379983453","doi":"https://doi.org/10.1007/s10208-023-09614-x"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-023-09614-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-023-09614-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09614-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09614-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5033277723","display_name":"Robert Szczelina","orcid":"https://orcid.org/0000-0001-7831-4577"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Robert Szczelina","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5085109355","display_name":"Piotr Zgliczy\u0144ski","orcid":"https://orcid.org/0000-0002-4852-0887"},"institutions":[{"id":"https://openalex.org/I126596746","display_name":"Jagiellonian University","ror":"https://ror.org/03bqmcz70","country_code":"PL","type":"education","lineage":["https://openalex.org/I126596746"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Piotr Zgliczy\u0144ski","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Jagiellonian University, \u0141ojasiewicza 6, 30-348, Krak\u00f3w, Poland","institution_ids":["https://openalex.org/I126596746"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5033277723"],"corresponding_institution_ids":["https://openalex.org/I126596746"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.9294,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.66101876,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"24","issue":"4","first_page":"1389","last_page":"1454"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10588","display_name":"Mathematical Dynamics and Fractals","score":0.9973999857902527,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10244","display_name":"Chaos control and synchronization","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7395857572555542},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.7161759734153748},{"id":"https://openalex.org/keywords/delay-differential-equation","display_name":"Delay differential equation","score":0.6183117032051086},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.548285186290741},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5358027219772339},{"id":"https://openalex.org/keywords/chaotic","display_name":"Chaotic","score":0.5201576352119446},{"id":"https://openalex.org/keywords/dynamical-systems-theory","display_name":"Dynamical systems theory","score":0.5117713809013367},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.5107190608978271},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.49164754152297974},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.482940137386322},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47598209977149963},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4470564126968384},{"id":"https://openalex.org/keywords/dynamical-system","display_name":"Dynamical system (definition)","score":0.44283390045166016},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4382566213607788},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.4271031618118286},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4244709610939026},{"id":"https://openalex.org/keywords/lorenz-system","display_name":"Lorenz system","score":0.41527533531188965},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34776702523231506},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3083440065383911},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17414090037345886}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7395857572555542},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.7161759734153748},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.6183117032051086},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.548285186290741},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5358027219772339},{"id":"https://openalex.org/C2777052490","wikidata":"https://www.wikidata.org/wiki/Q5072826","display_name":"Chaotic","level":2,"score":0.5201576352119446},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.5117713809013367},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5107190608978271},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.49164754152297974},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.482940137386322},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47598209977149963},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4470564126968384},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.44283390045166016},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4382566213607788},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.4271031618118286},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4244709610939026},{"id":"https://openalex.org/C151510863","wikidata":"https://www.wikidata.org/wiki/Q899844","display_name":"Lorenz system","level":3,"score":0.41527533531188965},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34776702523231506},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3083440065383911},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17414090037345886},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10208-023-09614-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-023-09614-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09614-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ruj.uj.edu.pl:item/430755","is_oa":true,"landing_page_url":"https://ruj.uj.edu.pl/handle/item/430755","pdf_url":"http://ruj.uj.edu.pl/bitstreams/7f3000c6-51a1-462b-bf5a-f9f95da528e8/download","source":{"id":"https://openalex.org/S4306401249","display_name":"Jagiellonian University Repository (Jagiellonian University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126596746","host_organization_name":"Jagiellonian University","host_organization_lineage":["https://openalex.org/I126596746"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.1007/s10208-023-09614-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-023-09614-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-023-09614-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.4399999976158142,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4379983453.pdf","grobid_xml":"https://content.openalex.org/works/W4379983453.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W313143230","https://openalex.org/W1667530050","https://openalex.org/W1964053068","https://openalex.org/W1967008192","https://openalex.org/W1967490525","https://openalex.org/W2003645160","https://openalex.org/W2045256358","https://openalex.org/W2060579120","https://openalex.org/W2082172869","https://openalex.org/W2086576641","https://openalex.org/W2094631910","https://openalex.org/W2121020818","https://openalex.org/W2207050309","https://openalex.org/W2556753600","https://openalex.org/W2596696916","https://openalex.org/W2762652717","https://openalex.org/W2962849511","https://openalex.org/W2963836683","https://openalex.org/W3070112433","https://openalex.org/W3093182962","https://openalex.org/W3120374098","https://openalex.org/W3171176617","https://openalex.org/W3182252275","https://openalex.org/W3186823439","https://openalex.org/W4206215385","https://openalex.org/W4206312007","https://openalex.org/W4213080596","https://openalex.org/W4214822274","https://openalex.org/W4221097285","https://openalex.org/W4237844826","https://openalex.org/W4247080625","https://openalex.org/W4254705978","https://openalex.org/W4289931307","https://openalex.org/W4301236970"],"related_works":["https://openalex.org/W2371448224","https://openalex.org/W3134495997","https://openalex.org/W2363680170","https://openalex.org/W2376428685","https://openalex.org/W4256082577","https://openalex.org/W625783435","https://openalex.org/W2799530996","https://openalex.org/W3114432406","https://openalex.org/W88762024","https://openalex.org/W2378004631"],"abstract_inverted_index":{"Abstract":[0],"We":[1,71],"present":[2],"a":[3,41,68,110],"Lohner-type":[4],"algorithm":[5,37],"for":[6,83],"rigorous":[7],"integration":[8],"of":[9,11,24,31,45,57,65,67,80,86,97,106],"systems":[10],"delay":[12],"differential":[13],"equations":[14],"(DDEs)":[15],"with":[16],"multiple":[17],"delays,":[18],"and":[19,52,104],"its":[20],"application":[21],"in":[22,48,60,91,109],"computation":[23],"Poincar\u00e9":[25],"maps,":[26],"to":[27,62,76],"study":[28],"the":[29,46,49,55,73,95],"dynamics":[30,108],"some":[32],"bounded,":[33],"eternal":[34],"solutions.":[35],"The":[36],"is":[38,101],"based":[39],"on":[40],"piecewise":[42],"Taylor":[43],"representation":[44],"solutions":[47,58,66],"phase":[50],"space,":[51],"it":[53],"exploits":[54],"smoothing":[56],"occurring":[59],"DDEs":[61],"produce":[63],"enclosures":[64],"high":[69],"order.":[70],"apply":[72],"topological":[74],"techniques":[75],"prove":[77],"various":[78],"kinds":[79],"dynamical":[81],"behaviour,":[82],"example,":[84],"existence":[85],"(apparently)":[87],"unstable":[88],"periodic":[89],"orbits":[90],"Mackey\u2013Glass":[92],"equation":[93],"(in":[94],"regime":[96],"parameters":[98],"where":[99],"chaos":[100],"numerically":[102],"observed)":[103],"persistence":[105],"symbolic":[107],"delay-perturbed":[111],"chaotic":[112],"ODE":[113],"(the":[114],"R\u00f6ssler":[115],"system).":[116]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-08-29T07:29:34.045763","created_date":"2025-10-10T00:00:00"}
