{"id":"https://openalex.org/W2158513140","doi":"https://doi.org/10.1137/140996719","title":"A Lyapunov-Type Theorem for Dissipative Numerical Integrators with Adaptive Time-Stepping","display_name":"A Lyapunov-Type Theorem for Dissipative Numerical Integrators with Adaptive Time-Stepping","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2158513140","doi":"https://doi.org/10.1137/140996719","mag":"2158513140"},"language":"en","primary_location":{"id":"doi:10.1137/140996719","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140996719","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/A5024259128","display_name":"Shun Sato","orcid":"https://orcid.org/0000-0002-8938-0825"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. Sato","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112086461","display_name":"T. Matsuo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Matsuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052378033","display_name":"Hideyuki Suzuki","orcid":"https://orcid.org/0000-0002-8150-140X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"H. Suzuki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5041780365","display_name":"Daisuke Furihata","orcid":"https://orcid.org/0000-0002-7849-6654"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. Furihata","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6698,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.8593481,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"53","issue":"6","first_page":"2505","last_page":"2518"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9994999766349792,"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/T11416","display_name":"Numerical methods for differential equations","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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","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":0.828437089920044},{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.7761611938476562},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.5640314221382141},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5406728386878967},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5253735780715942},{"id":"https://openalex.org/keywords/pullback-attractor","display_name":"Pullback attractor","score":0.4841080904006958},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4578413665294647},{"id":"https://openalex.org/keywords/discrete-time-and-continuous-time","display_name":"Discrete time and continuous time","score":0.45291706919670105},{"id":"https://openalex.org/keywords/attractor","display_name":"Attractor","score":0.41936996579170227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4178401827812195},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.36415088176727295},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.15945395827293396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12150585651397705},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11063608527183533},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06549456715583801}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.828437089920044},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.7761611938476562},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.5640314221382141},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5406728386878967},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5253735780715942},{"id":"https://openalex.org/C2778100799","wikidata":"https://www.wikidata.org/wiki/Q7259416","display_name":"Pullback attractor","level":3,"score":0.4841080904006958},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4578413665294647},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.45291706919670105},{"id":"https://openalex.org/C164380108","wikidata":"https://www.wikidata.org/wiki/Q507187","display_name":"Attractor","level":2,"score":0.41936996579170227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4178401827812195},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.36415088176727295},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.15945395827293396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12150585651397705},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11063608527183533},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06549456715583801},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/140996719","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140996719","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2298875045","display_name":"Construction of fundamental theory of difference method based on discrete function analysis and variational theory","funder_award_id":"25287030","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G6566097147","display_name":"A new development of mathematical theory of Discontinuous Galerkin FEM","funder_award_id":"15H03635","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G8888979278","display_name":"Construction of efficient structure-preserving methods for partial differential equations and its applications","funder_award_id":"26390126","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W91588129","https://openalex.org/W138308581","https://openalex.org/W192421812","https://openalex.org/W402518760","https://openalex.org/W563254532","https://openalex.org/W572187388","https://openalex.org/W611223367","https://openalex.org/W1496662771","https://openalex.org/W1516296361","https://openalex.org/W1532162288","https://openalex.org/W1535429593","https://openalex.org/W1541939020","https://openalex.org/W1557040331","https://openalex.org/W1559403043","https://openalex.org/W1578710616","https://openalex.org/W1594759473","https://openalex.org/W1802196594","https://openalex.org/W1964078443","https://openalex.org/W1965357780","https://openalex.org/W1966227249","https://openalex.org/W1969824994","https://openalex.org/W1979569363","https://openalex.org/W2000883601","https://openalex.org/W2003706036","https://openalex.org/W2007265214","https://openalex.org/W2013191941","https://openalex.org/W2022693520","https://openalex.org/W2023857920","https://openalex.org/W2024099978","https://openalex.org/W2029449803","https://openalex.org/W2043140935","https://openalex.org/W2046528357","https://openalex.org/W2058293744","https://openalex.org/W2062623397","https://openalex.org/W2070430318","https://openalex.org/W2070630372","https://openalex.org/W2071701027","https://openalex.org/W2085347462","https://openalex.org/W2091760807","https://openalex.org/W2100116001","https://openalex.org/W2154702089","https://openalex.org/W2156929097","https://openalex.org/W2613213377","https://openalex.org/W4237542901"],"related_works":["https://openalex.org/W2930130240","https://openalex.org/W2123378999","https://openalex.org/W2888124259","https://openalex.org/W2003779709","https://openalex.org/W2575361291","https://openalex.org/W2062327117","https://openalex.org/W2080177789","https://openalex.org/W913946616","https://openalex.org/W2084340197","https://openalex.org/W2557613019"],"abstract_inverted_index":{"The":[0],"asymptotic":[1,93],"behavior":[2,94],"of":[3,51,60,76,95,102],"continuous":[4,23],"dissipative":[5,8],"systems":[6],"and":[7,24,40,79],"numerical":[9],"integrators":[10,98],"with":[11],"fixed":[12],"time-stepping":[13,32,97],"can":[14,84],"be":[15,45],"fully":[16],"investigated":[17,46],"by":[18],"a":[19,68,73,86,103],"Lyapunov-type":[20,87],"theorem":[21],"on":[22],"discrete":[25,104],"dynamical":[26],"systems,":[27],"respectively.":[28],"However,":[29],"once":[30],"adaptive":[31,96],"is":[33],"involved,":[34],"such":[35,56],"theories":[36],"cease":[37],"to":[38,72],"work,":[39],"usually":[41],"the":[42,48,52,91,100],"dynamics":[43],"should":[44],"from":[47],"past,":[49],"instead":[50],"standard":[53],"forward":[54,74],"way,":[55],"as":[57],"in":[58,99],"terms":[59],"pullback":[61],"attractors.":[62],"In":[63],"this":[64],"paper,":[65],"we":[66,83],"present":[67],"different":[69],"approach---we":[70],"stick":[71],"definition":[75],"limit":[77],"sets":[78],"show":[80],"that":[81],"still":[82],"establish":[85],"theorem,":[88],"which":[89],"reveals":[90],"precise":[92],"presence":[101],"Lyapunov":[105],"functional.":[106]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-07-09T07:52:08.696243","created_date":"2025-10-10T00:00:00"}
