{"id":"https://openalex.org/W2037586851","doi":"https://doi.org/10.1137/s0036142998349527","title":"Nonlinear Stability Analysis of Area-Preserving Integrators","display_name":"Nonlinear Stability Analysis of Area-Preserving Integrators","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2037586851","doi":"https://doi.org/10.1137/s0036142998349527","mag":"2037586851"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998349527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998349527","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/A5049797937","display_name":"Robert D. Skeel","orcid":"https://orcid.org/0000-0002-4807-8988"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert D. Skeel","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5050692150","display_name":"K. Srinivas","orcid":"https://orcid.org/0009-0009-2669-725X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Srinivas","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5049797937"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6377,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.90053286,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"38","issue":"1","first_page":"129","last_page":"148"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9969000220298767,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9858999848365784,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8076153993606567},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.7605042457580566},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.7385385036468506},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6302343010902405},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5732512474060059},{"id":"https://openalex.org/keywords/midpoint","display_name":"Midpoint","score":0.5709145665168762},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5274867415428162},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.4761616885662079},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.4630814492702484},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4499262571334839},{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.4134315848350525},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.39485228061676025},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15546974539756775},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12495002150535583}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8076153993606567},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.7605042457580566},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7385385036468506},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6302343010902405},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5732512474060059},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.5709145665168762},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5274867415428162},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.4761616885662079},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.4630814492702484},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4499262571334839},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.4134315848350525},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39485228061676025},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15546974539756775},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12495002150535583},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142998349527","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998349527","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:T070300010471/7","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300010471/7&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":22,"referenced_works":["https://openalex.org/W125864753","https://openalex.org/W1524565983","https://openalex.org/W1569339351","https://openalex.org/W1662316386","https://openalex.org/W1983702722","https://openalex.org/W1989130537","https://openalex.org/W2004118536","https://openalex.org/W2008962126","https://openalex.org/W2023305549","https://openalex.org/W2034420901","https://openalex.org/W2039532283","https://openalex.org/W2041253741","https://openalex.org/W2049493974","https://openalex.org/W2059786425","https://openalex.org/W2062709451","https://openalex.org/W2094782434","https://openalex.org/W2126479355","https://openalex.org/W2162721376","https://openalex.org/W2198618549","https://openalex.org/W2550093246","https://openalex.org/W3022938717","https://openalex.org/W4211016790"],"related_works":["https://openalex.org/W2005694504","https://openalex.org/W2006096639","https://openalex.org/W3011672241","https://openalex.org/W1994054117","https://openalex.org/W2035154805","https://openalex.org/W70023880","https://openalex.org/W2105700337","https://openalex.org/W1530043903","https://openalex.org/W2150321577","https://openalex.org/W4289288125"],"abstract_inverted_index":{"Linear":[0],"stability":[1,64,143],"analysis":[2,29,65],"is":[3,45,99],"inadequate":[4],"for":[5,8,27,66,94,107,113],"integrators":[6],"designed":[7],"nondissipative":[9],"systems":[10,14],"such":[11],"as":[12],"Hamiltonian":[13,95],"in":[15,41],"which":[16,131],"nonlinear":[17,63],"effects":[18],"are":[19,111,145],"often":[20],"decisive.":[21],"Mathematical":[22],"theory":[23,90],"exists":[24],"(KAM":[25],"theory)":[26],"rigorous":[28,62],"of":[30,52,78,91,102,116,125,129,150,164,166],"small":[31],"perturbations":[32],"from":[33],"equilibria,":[34],"but":[35],"it":[36],"needs":[37],"to":[38,49,121],"be":[39],"expressed":[40],"a":[42,60,76,100,161],"form":[43],"that":[44,167],"more":[46,146],"easily":[47],"applicable":[48],"the":[50,71,89,114,122,126,133,135,139,156],"study":[51],"area-preserving":[53],"maps.":[54],"We":[55],"have":[56],"pursued":[57],"this,":[58],"obtaining":[59],"completely":[61],"elliptic":[67],"equilibria":[68],"based":[69],"on":[70],"Moser":[72],"twist":[73],"theorem":[74],"and":[75,80,104,119,138],"result":[77,98],"Cabral":[79],"Meyer":[81],"[Nonlinearity,":[82],"12":[83],"(1999),":[84],"pp.":[85],"1351--1362],":[86],"together":[87],"with":[88],"normal":[92],"forms":[93],"systems.":[96],"The":[97],"determination":[101],"necessary":[103],"sufficient":[105],"conditions":[106,110],"stability.":[108],"These":[109],"sharpened":[112],"case":[115],"reversible":[117],"maps":[118],"applied":[120],"symplectic":[123],"members":[124],"Newmark":[127],"family":[128],"integrators,":[130],"includes":[132],"leapfrog,":[134],"implicit":[136],"midpoint,":[137],"St\u00f6rmer--Cowell":[140],"methods.":[141],"Nonlinear":[142],"limits":[144],"severe":[147],"than":[148],"those":[149],"linear":[151,170],"theory.":[152],"As":[153],"an":[154],"example,":[155],"leapfrog":[157],"scheme":[158],"actually":[159],"has":[160],"step-size":[162],"limitation":[163],"71%":[165],"predicted":[168],"by":[169],"analysis.":[171]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}