{"id":"https://openalex.org/W2499526524","doi":"https://doi.org/10.1137/16m1085929","title":"On the Arbitrarily Long-Term Stability of Conservative Methods","display_name":"On the Arbitrarily Long-Term Stability of Conservative Methods","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2499526524","doi":"https://doi.org/10.1137/16m1085929","mag":"2499526524"},"language":"en","primary_location":{"id":"doi:10.1137/16m1085929","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1085929","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1607.06160","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Andy T. S. Wan","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andy T. S. Wan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Jean-Christophe Nave","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jean-Christophe Nave","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.367,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.76974907,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"56","issue":"5","first_page":"2751","last_page":"2775"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.6381000280380249,"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":0.6381000280380249,"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":0.06520000100135803,"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"}},{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.055799998342990875,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.8410000205039978},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.65420001745224},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.614799976348877},{"id":"https://openalex.org/keywords/conserved-quantity","display_name":"Conserved quantity","score":0.5346999764442444},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5342000126838684},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5073999762535095},{"id":"https://openalex.org/keywords/uniform-boundedness","display_name":"Uniform boundedness","score":0.4221000075340271},{"id":"https://openalex.org/keywords/bounded-deformation","display_name":"Bounded deformation","score":0.40790000557899475}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8629000186920166},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.8410000205039978},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.65420001745224},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.614799976348877},{"id":"https://openalex.org/C71914180","wikidata":"https://www.wikidata.org/wiki/Q1071013","display_name":"Conserved quantity","level":2,"score":0.5346999764442444},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5342000126838684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5113000273704529},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5073999762535095},{"id":"https://openalex.org/C90377204","wikidata":"https://www.wikidata.org/wiki/Q1052594","display_name":"Uniform boundedness","level":3,"score":0.4221000075340271},{"id":"https://openalex.org/C92928283","wikidata":"https://www.wikidata.org/wiki/Q4949981","display_name":"Bounded deformation","level":4,"score":0.40790000557899475},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3889000117778778},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3869999945163727},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3488999903202057},{"id":"https://openalex.org/C162392398","wikidata":"https://www.wikidata.org/wiki/Q272404","display_name":"Finite set","level":2,"score":0.33320000767707825},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3305000066757202},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.3208000063896179},{"id":"https://openalex.org/C175454919","wikidata":"https://www.wikidata.org/wiki/Q2342396","display_name":"Bounded operator","level":3,"score":0.3034999966621399},{"id":"https://openalex.org/C2778355321","wikidata":"https://www.wikidata.org/wiki/Q17079427","display_name":"Identity (music)","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.2648000121116638}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/16m1085929","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1085929","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:arXiv.org:1607.06160","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.06160","pdf_url":"https://arxiv.org/pdf/1607.06160","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1607.06160","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1607.06160","pdf_url":"https://arxiv.org/pdf/1607.06160","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320314331","display_name":"Centre de Recherches Math\u00e9matiques","ror":null},{"id":"https://openalex.org/F4320329205","display_name":"Banff International Research Station for Mathematical Innovation and Discovery","ror":null},{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W1565516854","https://openalex.org/W1600448051","https://openalex.org/W1912508791","https://openalex.org/W1964474305","https://openalex.org/W1965357780","https://openalex.org/W1969824994","https://openalex.org/W1980426569","https://openalex.org/W1992361999","https://openalex.org/W1995320858","https://openalex.org/W2003706036","https://openalex.org/W2006042718","https://openalex.org/W2010715349","https://openalex.org/W2028285252","https://openalex.org/W2041253741","https://openalex.org/W2043913140","https://openalex.org/W2062623397","https://openalex.org/W2074023170","https://openalex.org/W2083510019","https://openalex.org/W2085347462","https://openalex.org/W2121954553","https://openalex.org/W2138486270","https://openalex.org/W2149616747","https://openalex.org/W2157852777","https://openalex.org/W2170039048","https://openalex.org/W2560686802","https://openalex.org/W3099687355","https://openalex.org/W4213321166","https://openalex.org/W4292069163"],"related_works":[],"abstract_inverted_index":{"We":[0],"show":[1],"the":[2,22,25,35,43,54,66,115,132],"arbitrarily":[3,78],"long-term":[4,105,133],"stability":[5,106,134],"of":[6,15,24,38,74],"conservative":[7,40],"methods":[8],"for":[9,50,96],"autonomous":[10,16],"ODEs.":[11],"Given":[12],"a":[13,29],"system":[14],"ODEs":[17],"with":[18,42],"conserved":[19,26,98,117],"quantities,":[20],"if":[21],"preimage":[23],"quantities":[27,99,118],"possesses":[28],"bounded":[30,45,49,71],"locally":[31],"finite":[32,63],"neighborhood,":[33],"then":[34],"global":[36,67],"error":[37,68],"any":[39],"method":[41],"uniformly":[44],"displacement":[46],"property":[47],"is":[48,58,90,107],"all":[51],"time":[52,56,75,80,124],"when":[53,114],"uniform":[55],"step":[57],"taken":[59],"sufficiently":[60],"small.":[61],"On":[62],"precision":[64,84],"machines,":[65],"still":[69],"remains":[70],"and":[72,85],"independent":[73],"until":[76],"some":[77],"large":[79],"determined":[81],"by":[82],"machine":[83],"tolerance.":[86],"The":[87],"main":[88],"result":[89],"proved":[91],"using":[92,110],"elementary":[93],"topological":[94],"properties":[95],"discretized":[97,116],"which":[100],"are":[101,128],"equicontinuous.":[102],"In":[103],"particular,":[104],"also":[108],"shown":[109],"an":[111],"averaging":[112],"identity":[113],"do":[119],"not":[120],"explicitly":[121],"depend":[122],"on":[123],"steps.":[125],"Numerical":[126],"results":[127],"presented":[129],"to":[130],"illustrate":[131],"result.":[135]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-08-23T00:00:00"}