{"id":"https://openalex.org/W2080928083","doi":"https://doi.org/10.1137/050628143","title":"Stability Analysis of Large Time\u2010Stepping Methods for Epitaxial Growth Models","display_name":"Stability Analysis of Large Time\u2010Stepping Methods for Epitaxial Growth Models","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2080928083","doi":"https://doi.org/10.1137/050628143","mag":"2080928083"},"language":"en","primary_location":{"id":"doi:10.1137/050628143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628143","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/A5069580279","display_name":"Chuanju Xu","orcid":"https://orcid.org/0000-0002-6689-329X"},"institutions":[{"id":"https://openalex.org/I191208505","display_name":"Xiamen University","ror":"https://ror.org/00mcjh785","country_code":"CN","type":"education","lineage":["https://openalex.org/I191208505"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Chuanju Xu","raw_affiliation_strings":["Xiamen University"],"affiliations":[{"raw_affiliation_string":"Xiamen University","institution_ids":["https://openalex.org/I191208505"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058967726","display_name":"Tao Tang","orcid":"https://orcid.org/0000-0003-2919-2774"},"institutions":[{"id":"https://openalex.org/I530967","display_name":"Toronto Metropolitan University","ror":"https://ror.org/05g13zd79","country_code":"CA","type":"education","lineage":["https://openalex.org/I530967"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Tao Tang","raw_affiliation_strings":["Department of Mathematics"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics","institution_ids":["https://openalex.org/I530967"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5069580279"],"corresponding_institution_ids":["https://openalex.org/I191208505"],"apc_list":null,"apc_paid":null,"fwci":4.2447,"has_fulltext":false,"cited_by_count":384,"citation_normalized_percentile":{"value":0.94147857,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"44","issue":"4","first_page":"1759","last_page":"1779"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9984999895095825,"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"}},"topics":[{"id":"https://openalex.org/T12141","display_name":"Fluid Dynamics and Thin Films","score":0.9984999895095825,"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/T10591","display_name":"Theoretical and Computational Physics","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/3104","display_name":"Condensed Matter 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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.9957000017166138,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8909838795661926},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6174626350402832},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6127790808677673},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5607483386993408},{"id":"https://openalex.org/keywords/time-stepping","display_name":"Time stepping","score":0.5582818388938904},{"id":"https://openalex.org/keywords/work","display_name":"Work (physics)","score":0.5168817043304443},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4728389382362366},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.4368453919887543},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4358966052532196},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3735758364200592},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2386806607246399},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.22180333733558655},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11723443865776062},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07976967096328735}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8909838795661926},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6174626350402832},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6127790808677673},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5607483386993408},{"id":"https://openalex.org/C3019693144","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Time stepping","level":3,"score":0.5582818388938904},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.5168817043304443},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4728389382362366},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.4368453919887543},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4358966052532196},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3735758364200592},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2386806607246399},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.22180333733558655},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11723443865776062},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07976967096328735},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050628143","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050628143","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":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W64411513","https://openalex.org/W1549220217","https://openalex.org/W1605771617","https://openalex.org/W1805381866","https://openalex.org/W1969100313","https://openalex.org/W1975642142","https://openalex.org/W2000779144","https://openalex.org/W2008448937","https://openalex.org/W2008919294","https://openalex.org/W2016641139","https://openalex.org/W2020293658","https://openalex.org/W2020503418","https://openalex.org/W2025693807","https://openalex.org/W2029495360","https://openalex.org/W2043646756","https://openalex.org/W2048976031","https://openalex.org/W2057366524","https://openalex.org/W2064572062","https://openalex.org/W2066116321","https://openalex.org/W2068191335","https://openalex.org/W2073891868","https://openalex.org/W2089076027","https://openalex.org/W2104346351","https://openalex.org/W2152024595","https://openalex.org/W2168065659","https://openalex.org/W4240139632","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2102789413","https://openalex.org/W2131431484","https://openalex.org/W2096467061","https://openalex.org/W1532287630","https://openalex.org/W2940603871","https://openalex.org/W2082296130","https://openalex.org/W4299508867","https://openalex.org/W4226214462","https://openalex.org/W2028331352","https://openalex.org/W2475429613"],"abstract_inverted_index":{"Numerical":[0,90],"methods":[1,102],"for":[2,118],"solving":[3],"the":[4,8,11,66,69,76,80,84,97,108,119],"continuum":[5],"model":[6],"of":[7,10,31,51,68,83],"dynamics":[9],"molecular":[12],"beam":[13],"epitaxy":[14],"(MBE)":[15],"require":[16],"very":[17],"large":[18,23,112],"time":[19,24,41,47,70],"simulation,":[20],"and":[21,37,124],"therefore":[22],"steps":[25,48],"become":[26],"necessary.":[27],"The":[28,100,115],"main":[29],"purpose":[30],"this":[32,57],"work":[33],"is":[34,63,72],"to":[35,74,95,106],"construct":[36],"analyze":[38],"highly":[39],"stable":[40],"discretizations":[42],"which":[43,62],"allow":[44],"much":[45],"larger":[46],"than":[49],"those":[50],"a":[52],"standard":[53],"implicit\u2010explicit":[54],"approach.":[55],"To":[56],"end,":[58],"an":[59],"extra":[60],"term,":[61],"consistent":[64],"with":[65,111,127],"order":[67],"discretization,":[71],"added":[73],"stabilize":[75],"numerical":[77],"schemes.":[78],"Then":[79],"stability":[81],"properties":[82],"resulting":[85],"schemes":[86],"are":[87,92,103,122,125],"established":[88],"rigorously.":[89],"experiments":[91],"carried":[93],"out":[94],"support":[96],"theoretical":[98],"claims.":[99],"proposed":[101],"also":[104],"applied":[105],"simulate":[107],"MBE":[109],"models":[110],"solution":[113],"times.":[114],"power":[116],"laws":[117],"coarsening":[120],"process":[121],"obtained":[123],"compared":[126],"previously":[128],"published":[129],"results.":[130]},"counts_by_year":[{"year":2026,"cited_by_count":10},{"year":2025,"cited_by_count":35},{"year":2024,"cited_by_count":30},{"year":2023,"cited_by_count":43},{"year":2022,"cited_by_count":35},{"year":2021,"cited_by_count":38},{"year":2020,"cited_by_count":33},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":16},{"year":2017,"cited_by_count":25},{"year":2016,"cited_by_count":16},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":13},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
