{"id":"https://openalex.org/W4390949729","doi":"https://doi.org/10.1137/23m1554795","title":"A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations","display_name":"A Unified Design of Energy Stable Schemes with Variable Steps for Fractional Gradient Flows and Nonlinear Integro-differential Equations","publication_year":2024,"publication_date":"2024-01-17","ids":{"openalex":"https://openalex.org/W4390949729","doi":"https://doi.org/10.1137/23m1554795"},"language":"en","primary_location":{"id":"doi:10.1137/23m1554795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1554795","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5044562991","display_name":"Ren\u2010jun Qi","orcid":"https://orcid.org/0000-0003-2467-1354"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Ren-jun Qi","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, 210096, People\u2019s Republic of China","School of Mathematics, Southeast University, Nanjing, 210096, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, 210096, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76569877"]},{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, 210096, People's Republic of China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013656884","display_name":"Xuan Zhao","orcid":"https://orcid.org/0000-0002-3264-7197"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Zhao","raw_affiliation_strings":["Corresponding author. School of Mathematics, Southeast University, Nanjing, 210096, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-3264-7197","affiliations":[{"raw_affiliation_string":"Corresponding author. School of Mathematics, Southeast University, Nanjing, 210096, People\u2019s Republic of China","institution_ids":["https://openalex.org/I76569877"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5044562991"],"corresponding_institution_ids":["https://openalex.org/I76569877"],"apc_list":null,"apc_paid":null,"fwci":4.1945,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94098647,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"A130","last_page":"A155"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10104","display_name":"Nanofluid Flow and Heat Transfer","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.8203266859054565},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.672446608543396},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5895723700523376},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5207529067993164},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5121166706085205},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.48107051849365234},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.476365327835083},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.4615286886692047},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.41651687026023865},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41434842348098755},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10969328880310059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0845801830291748}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8203266859054565},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.672446608543396},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5895723700523376},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5207529067993164},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5121166706085205},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.48107051849365234},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.476365327835083},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.4615286886692047},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.41651687026023865},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41434842348098755},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10969328880310059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0845801830291748},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/23m1554795","is_oa":false,"landing_page_url":"https://doi.org/10.1137/23m1554795","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","score":0.8500000238418579,"id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G1506834623","display_name":null,"funder_award_id":"11861060","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4585534567","display_name":null,"funder_award_id":"61833005","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4647006287","display_name":null,"funder_award_id":"BK20222003","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G6876220824","display_name":null,"funder_award_id":"11701081","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8967878662","display_name":null,"funder_award_id":"U22B2046","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1964372262","https://openalex.org/W1972494090","https://openalex.org/W1992361999","https://openalex.org/W2005859257","https://openalex.org/W2014756735","https://openalex.org/W2049998327","https://openalex.org/W2065515432","https://openalex.org/W2066944044","https://openalex.org/W2081871678","https://openalex.org/W2110355045","https://openalex.org/W2118816806","https://openalex.org/W2140586964","https://openalex.org/W2526274843","https://openalex.org/W2731531705","https://openalex.org/W2766149883","https://openalex.org/W2796820619","https://openalex.org/W2893622182","https://openalex.org/W2964081326","https://openalex.org/W2964580220","https://openalex.org/W2990575151","https://openalex.org/W3018009055","https://openalex.org/W3024213355","https://openalex.org/W3030316402","https://openalex.org/W3033817112","https://openalex.org/W3084536940","https://openalex.org/W3089233602","https://openalex.org/W3094937669","https://openalex.org/W3106441075","https://openalex.org/W3174733916","https://openalex.org/W3184132380","https://openalex.org/W3188894086","https://openalex.org/W3195112625","https://openalex.org/W3195975264","https://openalex.org/W3199894888","https://openalex.org/W3205272164","https://openalex.org/W3209895642","https://openalex.org/W3215012796","https://openalex.org/W4220806789","https://openalex.org/W4241253766","https://openalex.org/W4285098199","https://openalex.org/W4287327908","https://openalex.org/W4294000657","https://openalex.org/W4313595089","https://openalex.org/W4372353560","https://openalex.org/W4381734946","https://openalex.org/W4387246044"],"related_works":["https://openalex.org/W2082446734","https://openalex.org/W4313560640","https://openalex.org/W4246784705","https://openalex.org/W2253351617","https://openalex.org/W2065284654","https://openalex.org/W4390948881","https://openalex.org/W912076904","https://openalex.org/W2161513111","https://openalex.org/W3164740183","https://openalex.org/W2525556503"],"abstract_inverted_index":{".A":[0],"unified":[1],"discrete":[2,46,82],"gradient":[3,47,74,167,173],"structure":[4],"of":[5,31,52,70,109],"the":[6,14,19,32,41,44,49,53,67,71,77,93,106,116,128,140,150,158,162],"second":[7],"order":[8],"nonuniform":[9],"integral":[10,22],"averaged":[11],"approximations":[12],"for":[13,105],"Caputo":[15],"fractional":[16,21,73,94,124,130,166],"derivative":[17],"and":[18,76,127],"Riemann\u2013Liouville":[20],"is":[23,35,60,64],"established":[24],"in":[25,40,161],"this":[26],"paper.":[27],"The":[28,81,122],"required":[29],"constraint":[30],"step-size":[33],"ratio":[34],"weaker":[36],"than":[37],"that":[38],"found":[39],"literature.":[42],"With":[43],"proposed":[45],"structure,":[48],"energy":[50,83],"stability":[51,107],"variable":[54,110,119],"step":[55,111],"Crank\u2013Nicolson":[56],"type":[57,120],"numerical":[58,112,147],"schemes":[59,113],"derived":[61],"immediately,":[62],"which":[63],"essential":[65],"to":[66,97,138,156],"long-time":[68],"simulations":[69],"time":[72,123,129,163,171],"flows":[75],"nonlinear":[78],"integro-differential":[79,169],"models.":[80],"dissipation":[84],"laws":[85],"fit":[86],"seamlessly":[87],"into":[88],"their":[89],"classical":[90],"counterparts":[91],"as":[92,135],"indexes":[95],"tend":[96],"one.":[98],"In":[99],"particular,":[100],"we":[101],"provide":[102],"a":[103],"framework":[104],"analysis":[108],"based":[114],"on":[115],"scalar":[117],"auxiliary":[118,175],"approaches.":[121],"Swift\u2013Hohenberg":[125],"model":[126,132],"sine-Gordon":[131],"are":[133,154],"taken":[134],"two":[136],"examples":[137],"elucidate":[139],"theoretical":[141,159],"results":[142,160],"at":[143],"great":[144],"length.":[145],"Extensive":[146],"experiments":[148],"using":[149],"adaptive":[151],"time-stepping":[152],"strategy":[153],"provided":[155],"verify":[157],"multiscale":[164],"simulations.Keywordstime":[165],"flownonlinear":[168],"equationnonuniform":[170],"stepsdiscrete":[172],"structurescalar":[174],"variableenergy":[176],"stabilityMSC":[177],"codes35Q9926A3365M7065M1235R11":[178]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
