{"id":"https://openalex.org/W2619423951","doi":"https://doi.org/10.1137/16m1089320","title":"Numerical Analysis of Nonlinear Subdiffusion Equations","display_name":"Numerical Analysis of Nonlinear Subdiffusion Equations","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2619423951","doi":"https://doi.org/10.1137/16m1089320","mag":"2619423951"},"language":"en","primary_location":{"id":"doi:10.1137/16m1089320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1089320","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":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98625/1/16m1089320.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039605463","display_name":"Bangti Jin","orcid":"https://orcid.org/0000-0002-3775-9155"},"institutions":[{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Bangti Jin","raw_affiliation_strings":["Department of Computer Science, University College London, London, WC1E 6BT, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, University College London, London, WC1E 6BT, UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039197834","display_name":"Buyang Li","orcid":"https://orcid.org/0000-0001-7566-3464"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Buyang Li","raw_affiliation_strings":["Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002445122","display_name":"Zhi Zhou","orcid":"https://orcid.org/0000-0002-3439-0313"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Zhi Zhou","raw_affiliation_strings":["Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039605463"],"corresponding_institution_ids":["https://openalex.org/I45129253"],"apc_list":null,"apc_paid":null,"fwci":15.472,"has_fulltext":true,"cited_by_count":245,"citation_normalized_percentile":{"value":0.99548376,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"56","issue":"1","first_page":"1","last_page":"23"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T10514","display_name":"Numerical methods in engineering","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9993000030517578,"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":0.9112532138824463},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6210079789161682},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6164597272872925},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6059625148773193},{"id":"https://openalex.org/keywords/uniqueness","display_name":"Uniqueness","score":0.6008639335632324},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5717827081680298},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5429044365882874},{"id":"https://openalex.org/keywords/gronwalls-inequality","display_name":"Gronwall's inequality","score":0.5155458450317383},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4434373080730438},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4386266767978668},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4180297255516052}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9112532138824463},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6210079789161682},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6164597272872925},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6059625148773193},{"id":"https://openalex.org/C2777021972","wikidata":"https://www.wikidata.org/wiki/Q22976830","display_name":"Uniqueness","level":2,"score":0.6008639335632324},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5717827081680298},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5429044365882874},{"id":"https://openalex.org/C37608338","wikidata":"https://www.wikidata.org/wiki/Q510733","display_name":"Gronwall's inequality","level":3,"score":0.5155458450317383},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4434373080730438},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4386266767978668},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4180297255516052},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/16m1089320","is_oa":false,"landing_page_url":"https://doi.org/10.1137/16m1089320","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:ira.lib.polyu.edu.hk:10397/98625","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/98625","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98625/1/16m1089320.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},{"id":"pmh:oai:eprints.ucl.ac.uk.OAI2:1561160","is_oa":false,"landing_page_url":"https://discovery.ucl.ac.uk/id/eprint/1561160/","pdf_url":null,"source":{"id":"https://openalex.org/S4306400024","display_name":"UCL Discovery (University College London)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45129253","host_organization_name":"University College London","host_organization_lineage":["https://openalex.org/I45129253"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"   SIAM Journal on Numerical Analysis , 56  (1)   pp. 1-23.   (2018)      ","raw_type":"Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/78024","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/78024","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/98625","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/98625","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98625/1/16m1089320.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"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":"Journal/Magazine Article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/10"}],"awards":[{"id":"https://openalex.org/G3552121337","display_name":null,"funder_award_id":"W911NF-15-1-0562","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3722276629","display_name":null,"funder_award_id":"EP/M025160/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G5316547286","display_name":null,"funder_award_id":"W911NF-15-1-056","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6334480233","display_name":null,"funder_award_id":"1-ZE6L","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7640431553","display_name":"Sparsity Regularization for Inverse Problems -- Theory, Algorithm and Application","funder_award_id":"EP/M025160/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G7913808730","display_name":null,"funder_award_id":"W911NF-15-1-0562","funder_id":"https://openalex.org/F4320333591","funder_display_name":"Multidisciplinary University Research Initiative"},{"id":"https://openalex.org/G8623470160","display_name":null,"funder_award_id":"AFOSR MURI","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G8944192383","display_name":null,"funder_award_id":"W911NF-15-1-0562","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"},{"id":"https://openalex.org/F4320333591","display_name":"Multidisciplinary University Research Initiative","ror":null},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2619423951.pdf"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W1965716945","https://openalex.org/W1967436950","https://openalex.org/W1968187902","https://openalex.org/W1969312973","https://openalex.org/W1991982189","https://openalex.org/W1998214447","https://openalex.org/W2002026218","https://openalex.org/W2012163408","https://openalex.org/W2028618557","https://openalex.org/W2041540906","https://openalex.org/W2042322027","https://openalex.org/W2048909372","https://openalex.org/W2053256951","https://openalex.org/W2056829543","https://openalex.org/W2065232540","https://openalex.org/W2070505112","https://openalex.org/W2071268148","https://openalex.org/W2073659542","https://openalex.org/W2074336586","https://openalex.org/W2093685032","https://openalex.org/W2111271983","https://openalex.org/W2138659615","https://openalex.org/W2165076033","https://openalex.org/W2168824372","https://openalex.org/W2187871078","https://openalex.org/W2243872394","https://openalex.org/W2274070693","https://openalex.org/W2435960546","https://openalex.org/W2437878828","https://openalex.org/W2963353751","https://openalex.org/W2964032975","https://openalex.org/W2964083141","https://openalex.org/W3122175143","https://openalex.org/W3148434010"],"related_works":["https://openalex.org/W143502885","https://openalex.org/W42113618","https://openalex.org/W2103468410","https://openalex.org/W2480115405","https://openalex.org/W3197542402","https://openalex.org/W1856228368","https://openalex.org/W2139321628","https://openalex.org/W2373343184","https://openalex.org/W3217078694","https://openalex.org/W2967022172"],"abstract_inverted_index":{"We":[0,50],"present":[1],"a":[2,18,32,52,80,90,95,133],"general":[3,53],"framework":[4],"for":[5,55,65,89,116],"the":[6,36,57,66,102,145,151,157,163],"rigorous":[7],"numerical":[8,164],"analysis":[9],"of":[10,21,35,47,105,128,156],"time-fractional":[11,91],"nonlinear":[12,48,97],"parabolic":[13],"partial":[14],"differential":[15],"equations,":[16],"with":[17,94,101],"fractional":[19,33,58],"derivative":[20],"order":[22,129],"$\\alpha\\in(0,1)$":[23],"in":[24],"time.":[25],"It":[26],"relies":[27],"on":[28,144,150],"three":[29],"technical":[30],"tools:":[31],"version":[34],"discrete":[37,41,59,106,124],"Gr\u00f6nwall":[38,60],"type":[39],"inequality,":[40],"maximal":[42,107],"regularity,":[43,88,108],"and":[44,62,69,87,122,136],"regularity":[45,142],"theory":[46],"equations.":[49],"establish":[51],"criterion":[54],"showing":[56],"inequality":[61],"verify":[63],"it":[64],"L1":[67],"scheme":[68],"convolution":[70],"quadrature":[71],"generated":[72],"by":[73,162],"backward":[74],"difference":[75],"formulas.":[76],"Further,":[77],"we":[78,109],"provide":[79],"complete":[81],"solution":[82,146],"theory,":[83],"e.g.,":[84],"existence,":[85],"uniqueness,":[86],"diffusion":[92],"equation":[93],"Lipschitz":[96],"source":[98],"term.":[99],"Together":[100],"known":[103],"results":[104],"derive":[110],"pointwise":[111],"$L^2(\\Omega)$":[112],"norm":[113],"error":[114],"estimates":[115],"semidiscrete":[117],"Galerkin":[118],"finite":[119],"element":[120],"solutions":[121],"fully":[123],"solutions,":[125],"which":[126],"are":[127],"$O(h^2)$":[130],"(up":[131],"to":[132],"logarithmic":[134],"factor)":[135],"$O(\\tau^\\alpha)$,":[137],"respectively,":[138],"without":[139],"any":[140],"extra":[141],"assumption":[143],"or":[147],"compatibility":[148],"condition":[149],"problem":[152],"data.":[153],"The":[154],"sharpness":[155],"convergence":[158],"rates":[159],"is":[160],"supported":[161],"experiments.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":33},{"year":2024,"cited_by_count":28},{"year":2023,"cited_by_count":35},{"year":2022,"cited_by_count":28},{"year":2021,"cited_by_count":35},{"year":2020,"cited_by_count":44},{"year":2019,"cited_by_count":31},{"year":2018,"cited_by_count":6}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}
