{"id":"https://openalex.org/W2302272192","doi":"https://doi.org/10.1137/15m1019301","title":"Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients","display_name":"Fast Finite Difference Approximation for Identifying Parameters in a Two-dimensional Space-fractional Nonlocal Model with Variable Diffusivity Coefficients","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2302272192","doi":"https://doi.org/10.1137/15m1019301","mag":"2302272192"},"language":"en","primary_location":{"id":"doi:10.1137/15m1019301","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019301","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/A5101833958","display_name":"S. Chen","orcid":"https://orcid.org/0000-0003-3165-0674"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"S. Chen","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011004372","display_name":"F. Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"F. Liu","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055362302","display_name":"Xiaoyun Jiang","orcid":"https://orcid.org/0000-0003-2305-9526"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"X. Jiang","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007130769","display_name":"Ian Turner","orcid":"https://orcid.org/0000-0003-2794-3968"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"I. Turner","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5003330950","display_name":"Kevin Burrage","orcid":"https://orcid.org/0000-0002-8111-1137"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Burrage","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5101833958"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.1397,"has_fulltext":false,"cited_by_count":52,"citation_normalized_percentile":{"value":0.97826427,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"54","issue":"2","first_page":"606","last_page":"624"},"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":0.9997000098228455,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9983999729156494,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.7771768569946289},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6022486686706543},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.5631311535835266},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5526911020278931},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4888536334037781},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.45225903391838074},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43374839425086975},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4285953640937805},{"id":"https://openalex.org/keywords/line-search","display_name":"Line search","score":0.4247216582298279},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3394858241081238},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2705105245113373},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1135033667087555}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7771768569946289},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6022486686706543},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.5631311535835266},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5526911020278931},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4888536334037781},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.45225903391838074},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43374839425086975},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4285953640937805},{"id":"https://openalex.org/C85522705","wikidata":"https://www.wikidata.org/wiki/Q3278015","display_name":"Line search","level":3,"score":0.4247216582298279},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3394858241081238},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2705105245113373},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1135033667087555},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C178635117","wikidata":"https://www.wikidata.org/wiki/Q747499","display_name":"RADIUS","level":2,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1019301","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019301","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1970573106","https://openalex.org/W1976739005","https://openalex.org/W1986544454","https://openalex.org/W1988571032","https://openalex.org/W1996054002","https://openalex.org/W2001744739","https://openalex.org/W2002245931","https://openalex.org/W2011587687","https://openalex.org/W2014101152","https://openalex.org/W2016680653","https://openalex.org/W2019324632","https://openalex.org/W2030146312","https://openalex.org/W2037973974","https://openalex.org/W2039076597","https://openalex.org/W2041393921","https://openalex.org/W2041540906","https://openalex.org/W2043080303","https://openalex.org/W2046631971","https://openalex.org/W2051216605","https://openalex.org/W2053946502","https://openalex.org/W2055962432","https://openalex.org/W2056061743","https://openalex.org/W2057748165","https://openalex.org/W2058075916","https://openalex.org/W2061684894","https://openalex.org/W2072825472","https://openalex.org/W2083644096","https://openalex.org/W2084791898","https://openalex.org/W2086414613","https://openalex.org/W2105723279","https://openalex.org/W2107162131","https://openalex.org/W2112900014","https://openalex.org/W2114010261","https://openalex.org/W2115176036","https://openalex.org/W2120862100","https://openalex.org/W2140620666","https://openalex.org/W2143004014","https://openalex.org/W2155216327","https://openalex.org/W2162592888","https://openalex.org/W2170885741","https://openalex.org/W2185071224","https://openalex.org/W2318735192","https://openalex.org/W3103136962","https://openalex.org/W4230205099"],"related_works":["https://openalex.org/W2349115186","https://openalex.org/W2351994672","https://openalex.org/W2173575616","https://openalex.org/W2350706414","https://openalex.org/W2968025875","https://openalex.org/W2053799091","https://openalex.org/W937190428","https://openalex.org/W2000705372","https://openalex.org/W2274598647","https://openalex.org/W3015030348"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,34,62,86,118],"consider":[4],"an":[5,36],"inverse":[6,160],"problem":[7,44,161],"for":[8,41,56,158],"identifying":[9],"the":[10,25,42,46,51,57,60,82,88,95,106,114,125,130,145,148,156,159,163],"fractional":[11],"derivative":[12],"indices":[13],"in":[14,74],"a":[15,22,64],"two-dimensional":[16],"space-fractional":[17,164],"nonlocal":[18],"model":[19,111,166],"based":[20],"on":[21],"generalization":[23],"of":[24,50,59,129,147,155],"two-sided":[26],"Riemann--Liouville":[27],"formulation":[28],"with":[29,94,113,136],"variable":[30],"diffusivity":[31],"coefficients.":[32],"First,":[33],"derive":[35],"implicit":[37],"difference":[38],"method":[39,69],"(IDM)":[40],"direct":[43],"and":[45,48,80,127,140],"stability":[47],"convergence":[49,153],"IDM":[52],"are":[53,134],"discussed.":[54],"Second,":[55],"implementation":[58],"IDM,":[61],"develop":[63],"fast":[65],"bi-conjugate":[66],"gradient":[67],"stabilized":[68],"(FBi-CGSTAB)":[70],"that":[71],"is":[72,167],"superior":[73],"computational":[75],"performance":[76],"to":[77,104,123,143],"Gaussian":[78],"elimination":[79],"attains":[81],"same":[83],"accuracy.":[84],"Third,":[85],"utilize":[87],"Levenberg--Marquardt":[89],"(L-M)":[90],"regularization":[91,150],"technique":[92],"combined":[93],"Armijo":[96],"rule":[97],"(the":[98],"popular":[99],"inexact":[100],"line":[101],"search":[102],"condition)":[103],"solve":[105],"modified":[107],"nonlinear":[108],"least":[109],"squares":[110],"associated":[112],"parameter":[115],"identification.":[116],"Finally,":[117],"carry":[119],"out":[120],"numerical":[121],"tests":[122],"verify":[124],"accuracy":[126],"efficiency":[128],"IDM.":[131],"Numerical":[132],"investigations":[133],"performed":[135],"both":[137],"accurate":[138],"data":[139,142],"noisy":[141],"check":[144],"effectiveness":[146],"L-M":[149,157],"method.":[151],"The":[152],"behavior":[154],"involving":[162],"diffusion":[165],"shown":[168],"graphically.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":13},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
