{"id":"https://openalex.org/W2948777523","doi":"https://doi.org/10.1137/18m1194328","title":"On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance","display_name":"On the Variable Two-Step IMEX BDF Method for Parabolic Integro-differential Equations with Nonsmooth Initial Data Arising in Finance","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2948777523","doi":"https://doi.org/10.1137/18m1194328","mag":"2948777523"},"language":"en","primary_location":{"id":"doi:10.1137/18m1194328","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194328","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/A5014198183","display_name":"Wansheng Wang","orcid":"https://orcid.org/0000-0002-2128-7501"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wansheng Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047526920","display_name":"Yingzi Chen","orcid":"https://orcid.org/0000-0001-7275-781X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yingzi Chen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100646825","display_name":"Fang Hua","orcid":"https://orcid.org/0000-0003-2465-4888"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hua Fang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.6315,"has_fulltext":false,"cited_by_count":95,"citation_normalized_percentile":{"value":0.9808502,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"57","issue":"3","first_page":"1289","last_page":"1317"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9988999962806702,"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"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9988999962806702,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9970999956130981,"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"}},{"id":"https://openalex.org/T11829","display_name":"Mathematical Biology Tumor Growth","score":0.948199987411499,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8342243432998657},{"id":"https://openalex.org/keywords/jump-diffusion","display_name":"Jump diffusion","score":0.7695823907852173},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.7201467156410217},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5377334356307983},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.512665867805481},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5123437643051147},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.46352773904800415},{"id":"https://openalex.org/keywords/differential","display_name":"Differential (mechanical device)","score":0.4531160295009613},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.4132496118545532},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32217270135879517},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.295534610748291},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.08719110488891602}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8342243432998657},{"id":"https://openalex.org/C2779664328","wikidata":"https://www.wikidata.org/wiki/Q6311158","display_name":"Jump diffusion","level":3,"score":0.7695823907852173},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.7201467156410217},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5377334356307983},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.512665867805481},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5123437643051147},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.46352773904800415},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.4531160295009613},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.4132496118545532},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32217270135879517},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.295534610748291},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.08719110488891602},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace 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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/18m1194328","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194328","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":[{"id":"https://openalex.org/G1506495766","display_name":null,"funder_award_id":"11371074","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7972601977","display_name":null,"funder_award_id":"11771060","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/F4320332873","display_name":"Society for Community Research and Action","ror":"https://ror.org/00rt1d436"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1940115485","https://openalex.org/W1971954987","https://openalex.org/W1980666017","https://openalex.org/W1994111439","https://openalex.org/W2000419761","https://openalex.org/W2024994261","https://openalex.org/W2030940697","https://openalex.org/W2040394324","https://openalex.org/W2049599235","https://openalex.org/W2053384289","https://openalex.org/W2061802455","https://openalex.org/W2063164826","https://openalex.org/W2076959590","https://openalex.org/W2077791698","https://openalex.org/W2079233604","https://openalex.org/W2079518554","https://openalex.org/W2081787832","https://openalex.org/W2090708196","https://openalex.org/W2115086321","https://openalex.org/W2133435652","https://openalex.org/W2133516011","https://openalex.org/W2138540172","https://openalex.org/W2142278738","https://openalex.org/W2151065060","https://openalex.org/W2157094572","https://openalex.org/W2159074954","https://openalex.org/W2161836471","https://openalex.org/W2163282685","https://openalex.org/W2368861806","https://openalex.org/W2507251664","https://openalex.org/W2513339681","https://openalex.org/W2518948376","https://openalex.org/W2558203600","https://openalex.org/W2607049963","https://openalex.org/W2918281123","https://openalex.org/W2964266327","https://openalex.org/W3122167020","https://openalex.org/W3124053904","https://openalex.org/W3124062437","https://openalex.org/W4231057775"],"related_works":["https://openalex.org/W2648988829","https://openalex.org/W2507439616","https://openalex.org/W2998311464","https://openalex.org/W3124741583","https://openalex.org/W362430865","https://openalex.org/W2954755983","https://openalex.org/W2362743624","https://openalex.org/W3121278253","https://openalex.org/W3192755727","https://openalex.org/W2390566486"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"the":[3,17,20,34,45,63,70,74,79,101,107,120,125,128,134,137],"implicit-explicit":[4],"(IMEX)":[5],"two-step":[6],"backward":[7],"differentiation":[8],"formula":[9],"(BDF2)":[10],"method":[11,50,84,139],"with":[12],"variable":[13,46,80],"step-size,":[14],"due":[15],"to":[16],"nonsmoothness":[18,126],"of":[19,67,124,127,136],"initial":[21],"data,":[22],"is":[23,42,51,104,116],"developed":[24],"for":[25,53,78,140],"solving":[26],"parabolic":[27],"partial":[28],"integro-differential":[29],"equations":[30],"(PIDEs),":[31],"which":[32],"describe":[33],"jump-diffusion":[35,146],"option":[36],"pricing":[37],"model":[38],"in":[39],"finance.":[40],"It":[41],"shown":[43],"that":[44],"step-size":[47,81],"IMEX":[48,82],"BDF2":[49,83],"stable":[52],"abstract":[54,68],"PIDEs":[55],"under":[56,145],"suitable":[57],"time":[58,64,88],"step":[59],"restrictions.":[60],"Based":[61],"on":[62],"regularity":[65],"analysis":[66],"PIDEs,":[69],"consistency":[71],"error":[72,76],"and":[73,100,142],"global":[75],"bounds":[77],"are":[85,93],"provided.":[86],"After":[87],"semidiscretization,":[89],"spatial":[90],"differential":[91],"operators":[92],"treated":[94],"by":[95],"using":[96,106],"finite":[97],"difference":[98],"methods,":[99],"jump":[102],"integral":[103],"computed":[105],"composite":[108],"trapezoidal":[109],"rule.":[110],"A":[111],"local":[112],"mesh":[113],"refinement":[114],"strategy":[115],"also":[117],"considered":[118],"near":[119],"strike":[121],"price":[122],"because":[123],"payoff":[129],"function.":[130],"Numerical":[131],"results":[132],"illustrate":[133],"effectiveness":[135],"proposed":[138],"European":[141],"American":[143],"options":[144],"models.":[147]},"counts_by_year":[{"year":2026,"cited_by_count":9},{"year":2025,"cited_by_count":23},{"year":2024,"cited_by_count":15},{"year":2023,"cited_by_count":14},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":12},{"year":2019,"cited_by_count":4}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}
