{"id":"https://openalex.org/W4386377660","doi":"https://doi.org/10.1080/00207160.2023.2254412","title":"A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black\u2013Scholes model","display_name":"A fast compact difference scheme with unequal time-steps for the tempered time-fractional Black\u2013Scholes model","publication_year":2023,"publication_date":"2023-09-01","ids":{"openalex":"https://openalex.org/W4386377660","doi":"https://doi.org/10.1080/00207160.2023.2254412"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2023.2254412","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2023.2254412","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5036665467","display_name":"Jinfeng Zhou","orcid":"https://orcid.org/0000-0003-2479-3968"},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]},{"id":"https://openalex.org/I4210110849","display_name":"Sichuan Tourism University","ror":"https://ror.org/018rwb805","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210110849"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinfeng Zhou","raw_affiliation_strings":["College of Big Data and Statistics, Sichuan Tourism University, Chengdu, Sichuan, People's Republic of China","School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Big Data and Statistics, Sichuan Tourism University, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I4210110849"]},{"raw_affiliation_string":"School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I204831749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079893028","display_name":"Xian\u2010Ming Gu","orcid":"https://orcid.org/0000-0001-7895-2050"},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xian-Ming Gu","raw_affiliation_strings":["School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Southwestern University of Finance and Economics, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I204831749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080562594","display_name":"Yongliang Zhao","orcid":"https://orcid.org/0000-0003-0121-1312"},"institutions":[{"id":"https://openalex.org/I63354593","display_name":"Sichuan Normal University","ror":"https://ror.org/043dxc061","country_code":"CN","type":"education","lineage":["https://openalex.org/I63354593"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yong-Liang Zhao","raw_affiliation_strings":["School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Sichuan Normal University, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I63354593"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100444599","display_name":"Hu Li","orcid":"https://orcid.org/0000-0001-8624-8792"},"institutions":[{"id":"https://openalex.org/I4210147228","display_name":"Chengdu Normal University","ror":"https://ror.org/04enz2k98","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147228"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hu Li","raw_affiliation_strings":["School of Mathematics, Chengdu Normal University, Chengdu, Sichuan, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics, Chengdu Normal University, Chengdu, Sichuan, People's Republic of China","institution_ids":["https://openalex.org/I4210147228"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5079893028"],"corresponding_institution_ids":["https://openalex.org/I204831749"],"apc_list":null,"apc_paid":null,"fwci":4.4417,"has_fulltext":false,"cited_by_count":20,"citation_normalized_percentile":{"value":0.95122681,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"101","issue":"9-10","first_page":"989","last_page":"1011"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10541","display_name":"Nonlinear Differential Equations Analysis","score":0.9973000288009644,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10067","display_name":"Stochastic processes and financial applications","score":0.995199978351593,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7366644740104675},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6333912014961243},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.52752286195755},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4343945384025574},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4323437809944153},{"id":"https://openalex.org/keywords/black\u2013scholes-model","display_name":"Black\u2013Scholes model","score":0.424930214881897},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.422902375459671},{"id":"https://openalex.org/keywords/finance","display_name":"Finance","score":0.10871097445487976}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7366644740104675},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6333912014961243},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.52752286195755},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4343945384025574},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4323437809944153},{"id":"https://openalex.org/C163128081","wikidata":"https://www.wikidata.org/wiki/Q1338307","display_name":"Black\u2013Scholes model","level":3,"score":0.424930214881897},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.422902375459671},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.10871097445487976},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.0},{"id":"https://openalex.org/C91602232","wikidata":"https://www.wikidata.org/wiki/Q756115","display_name":"Volatility (finance)","level":2,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","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},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2023.2254412","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2023.2254412","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3573903317","display_name":null,"funder_award_id":"2020YJ0007","funder_id":"https://openalex.org/F4320333337","funder_display_name":"Applied Basic Research Program of Sichuan Province"}],"funders":[{"id":"https://openalex.org/F4320333337","display_name":"Applied Basic Research Program of Sichuan Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1965277094","https://openalex.org/W1968898906","https://openalex.org/W2041540906","https://openalex.org/W2050128975","https://openalex.org/W2105376214","https://openalex.org/W2138534521","https://openalex.org/W2143623732","https://openalex.org/W2157094572","https://openalex.org/W2202617566","https://openalex.org/W2294758632","https://openalex.org/W2295905769","https://openalex.org/W2315653911","https://openalex.org/W2339759570","https://openalex.org/W2547517016","https://openalex.org/W2608656286","https://openalex.org/W2613190027","https://openalex.org/W2625182672","https://openalex.org/W2733082216","https://openalex.org/W2794314669","https://openalex.org/W2794616828","https://openalex.org/W2799821673","https://openalex.org/W2898829002","https://openalex.org/W2899491063","https://openalex.org/W2903218532","https://openalex.org/W2955920149","https://openalex.org/W2956035471","https://openalex.org/W2963309992","https://openalex.org/W2989202487","https://openalex.org/W3023631506","https://openalex.org/W3033767560","https://openalex.org/W3035229577","https://openalex.org/W3096050333","https://openalex.org/W3097393452","https://openalex.org/W3098148926","https://openalex.org/W3098333777","https://openalex.org/W3110217938","https://openalex.org/W3122167020","https://openalex.org/W3129922278","https://openalex.org/W3141805168","https://openalex.org/W3176595871","https://openalex.org/W3215725018","https://openalex.org/W4229825750","https://openalex.org/W4238187298","https://openalex.org/W4286470391","https://openalex.org/W4289525644","https://openalex.org/W4290547600","https://openalex.org/W4312911196","https://openalex.org/W4317395172","https://openalex.org/W4321460201","https://openalex.org/W6642220840","https://openalex.org/W6704084187","https://openalex.org/W6910531181"],"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/W3121927021","https://openalex.org/W2021368388","https://openalex.org/W2000813003","https://openalex.org/W1974525074"],"abstract_inverted_index":{"AbstractThe":[0],"Black\u2013Scholes":[1],"(B\u2013S)":[2],"equation":[3],"has":[4],"been":[5],"recently":[6],"extended":[7],"as":[8],"a":[9,30,107],"kind":[10],"of":[11,38,56,79,125,189,229,247],"tempered":[12,40,96],"time-fractional":[13,41,130],"B\u2013S":[14,42,131],"equations,":[15],"which":[16,104],"becomes":[17],"an":[18],"interesting":[19],"mathematical":[20],"model":[21],"in":[22,48,94,212,223],"option":[23],"pricing.":[24],"In":[25],"this":[26],"study,":[27],"we":[28,59],"provide":[29],"fast":[31,108],"numerical":[32,75,120],"method":[33,113],"to":[34,72,86,106,147,165,183,197,207],"approximate":[35],"the":[36,39,52,61,74,80,91,95,116,123,126,167,194,209,213,230,242,254],"solution":[37],"model.":[43],"To":[44],"achieve":[45],"high-order":[46],"accuracy":[47],"space":[49],"and":[50,154,161,202,253,257,263],"overcome":[51],"weak":[53],"initial":[54],"singularity":[55],"exact":[57],"solution,":[58],"combine":[60],"compact":[62,111],"difference":[63,82,112,136],"operator":[64],"with":[65,233],"L1-type":[66],"approximation":[67],"under":[68],"nonuniform":[69],"time":[70,133],"steps":[71],"yield":[73],"scheme.":[76],"The":[77],"convergence":[78],"proposed":[81,127],"scheme":[83],"is":[84,100,205],"proved":[85],"be":[87],"unconditionally":[88,109],"stable.":[89],"Moreover,":[90],"kernel":[92],"function":[93,232],"Caputo":[97],"fractional":[98],"derivative":[99],"approximated":[101],"by":[102,193,241],"sum-of-exponentials,":[103],"leads":[105],"stable":[110],"that":[114],"reduces":[115],"computational":[117],"cost.":[118],"Finally,":[119],"results":[121,222],"demonstrate":[122],"effectiveness":[124],"methods.Keywords:":[128],"Tempered":[129],"modelnonuniform":[132],"stepsexponential":[134],"transformationcompact":[135],"schemeweak":[137],"regularity2020":[138],"AMS":[139],"Subject":[140],"Classifications:":[141],"65M0665M5026A3391G20":[142],"AcknowledgmentsThe":[143],"authors":[144],"would":[145],"like":[146],"thank":[148],"anonymous":[149],"reviewers,":[150],"Dr.":[151,155],"Can":[152],"Li":[153],"Jinye":[156],"Shen":[157],"whose":[158],"insightful":[159],"comments":[160],"careful":[162],"proof-checks":[163],"helped":[164],"improve":[166],"current":[168],"paper.":[169],"X.-M.":[170],"Gu":[171],"also":[172],"thanks":[173],"Prof.":[174],"Dongling":[175],"Wang":[176],"for":[177],"helpful":[178],"discussions":[179],"during":[180],"his":[181],"visiting":[182],"Xiangtan":[184],"University.Disclosure":[185],"statementNo":[186],"potential":[187],"conflict":[188],"interest":[190],"was":[191,239],"reported":[192],"author(s).Notes1":[195],"Due":[196],"two":[198],"known":[199],"functions":[200],"\u03d5(\u03c4)":[201],"\u03c6(\u03c4),":[203],"it":[204],"easy":[206],"compute":[208],"term":[210],"0CD\u03c4\u03b1,\u03bbz(x,\u03c4)":[211],"analytical":[214],"(or":[215],"numerical)":[216],"manner.2":[217],"See":[218],"some":[219],"related":[220],"experimental":[221],"our":[224],"arXiv":[225],"preprint":[226],"https://arxiv.org/abs/2303.10592v2.3":[227],"Evaluation":[228],"M-L":[231],"2":[234],"parameters:":[235],"https://www.mathworks.com/matlabcentral/fileexchange/48154-the-mittag-leffler-function.Additional":[236],"informationFundingThis":[237],"work":[238],"supported":[240],"Applied":[243],"Basic":[244],"Research":[245],"Program":[246,259],"Sichuan":[248,255],"Province":[249],"[grant":[250,260],"number":[251,261,265],"2020YJ0007]":[252],"Science":[256],"Technology":[258],"2022ZYD0006":[262],"grant":[264],"2023NSFSC1326].":[266]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
