{"id":"https://openalex.org/W2020930183","doi":"https://doi.org/10.1137/030602617","title":"Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance","display_name":"Fast Numerical Solution of Parabolic Integrodifferential Equations with Applications in Finance","publication_year":2005,"publication_date":"2005-01-01","ids":{"openalex":"https://openalex.org/W2020930183","doi":"https://doi.org/10.1137/030602617","mag":"2020930183"},"language":"en","primary_location":{"id":"doi:10.1137/030602617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602617","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":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/6144161a-016f-4377-9004-c5888eb5ecc8/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089699052","display_name":"Ana-Maria Matache","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210111868","display_name":"Zurich University of Teacher Education","ror":"https://ror.org/01awgk221","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210111868"]}],"countries":["CH","US"],"is_corresponding":true,"raw_author_name":"Ana-Maria Matache","raw_affiliation_strings":["SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"]},{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110448103","display_name":"Christoph Schwab","orcid":null},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210111868","display_name":"Zurich University of Teacher Education","ror":"https://ror.org/01awgk221","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210111868"]}],"countries":["CH","US"],"is_corresponding":false,"raw_author_name":"Christoph Schwab","raw_affiliation_strings":["SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"]},{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081674944","display_name":"Thomas P. Wihler","orcid":"https://orcid.org/0000-0003-1232-0637"},"institutions":[{"id":"https://openalex.org/I130238516","display_name":"University of Minnesota","ror":"https://ror.org/017zqws13","country_code":"US","type":"education","lineage":["https://openalex.org/I130238516"]},{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]},{"id":"https://openalex.org/I4210090941","display_name":"Institute for Biomedical Engineering","ror":"https://ror.org/00baskk38","country_code":"CH","type":"facility","lineage":["https://openalex.org/I202697423","https://openalex.org/I2799323385","https://openalex.org/I35440088","https://openalex.org/I4210090941"]},{"id":"https://openalex.org/I4210111868","display_name":"Zurich University of Teacher Education","ror":"https://ror.org/01awgk221","country_code":"CH","type":"education","lineage":["https://openalex.org/I4210111868"]}],"countries":["CH","US"],"is_corresponding":false,"raw_author_name":"Thomas P. Wihler","raw_affiliation_strings":["SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND"],"affiliations":[{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS AND RISKLAB, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088"]},{"raw_affiliation_string":"SCHOOL OF MATHEMATICS, UNIVERSITY OF MINNESOTA, MINNEAPOLIS MN, 55455, USA","institution_ids":["https://openalex.org/I130238516"]},{"raw_affiliation_string":"SEMINAR FOR APPLIED MATHEMATICS, ETH Z\u00dcRICH, 8092 Z\u00dcRICH, SWITZERLAND","institution_ids":["https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089699052"],"corresponding_institution_ids":["https://openalex.org/I130238516","https://openalex.org/I35440088","https://openalex.org/I4210090941","https://openalex.org/I4210111868"],"apc_list":null,"apc_paid":null,"fwci":8.9658,"has_fulltext":true,"cited_by_count":86,"citation_normalized_percentile":{"value":0.97837467,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"27","issue":"2","first_page":"369","last_page":"393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9977999925613403,"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":0.9977999925613403,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9958999752998352,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9900000095367432,"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":0.837194561958313},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.727624237537384},{"id":"https://openalex.org/keywords/degrees-of-freedom","display_name":"Degrees of freedom (physics and chemistry)","score":0.5630630850791931},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5438036322593689},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.535322368144989},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.5325894355773926},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.5236582159996033},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48938220739364624},{"id":"https://openalex.org/keywords/interval","display_name":"Interval (graph theory)","score":0.47004571557044983},{"id":"https://openalex.org/keywords/elliptic-operator","display_name":"Elliptic operator","score":0.4682152271270752},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4375193119049072},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.41873496770858765},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41634631156921387},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.2136232852935791},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.1693524420261383},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07023385167121887}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.837194561958313},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.727624237537384},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.5630630850791931},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5438036322593689},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.535322368144989},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.5325894355773926},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.5236582159996033},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48938220739364624},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.47004571557044983},{"id":"https://openalex.org/C70610323","wikidata":"https://www.wikidata.org/wiki/Q427625","display_name":"Elliptic operator","level":2,"score":0.4682152271270752},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4375193119049072},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.41873496770858765},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41634631156921387},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.2136232852935791},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.1693524420261383},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07023385167121887},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/030602617","is_oa":false,"landing_page_url":"https://doi.org/10.1137/030602617","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"},{"id":"pmh:oai:conservancy.umn.edu:11299/4004","is_oa":true,"landing_page_url":"http://purl.umn.edu/4004","pdf_url":"https://conservancy.umn.edu/bitstreams/6144161a-016f-4377-9004-c5888eb5ecc8/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/4004","is_oa":true,"landing_page_url":"http://purl.umn.edu/4004","pdf_url":"https://conservancy.umn.edu/bitstreams/6144161a-016f-4377-9004-c5888eb5ecc8/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020930183.pdf","grobid_xml":"https://content.openalex.org/works/W2020930183.grobid-xml"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W6253552","https://openalex.org/W1499969990","https://openalex.org/W1509975853","https://openalex.org/W1525526370","https://openalex.org/W1531532214","https://openalex.org/W1539855477","https://openalex.org/W1597209545","https://openalex.org/W1659099958","https://openalex.org/W1967203400","https://openalex.org/W1968759608","https://openalex.org/W1975414548","https://openalex.org/W1975760144","https://openalex.org/W1994858552","https://openalex.org/W2008222077","https://openalex.org/W2039963627","https://openalex.org/W2042775870","https://openalex.org/W2063164826","https://openalex.org/W2064216226","https://openalex.org/W2077791698","https://openalex.org/W2100190417","https://openalex.org/W2138540172","https://openalex.org/W2142278738","https://openalex.org/W2147035016","https://openalex.org/W2148688139","https://openalex.org/W2151065060","https://openalex.org/W2169797654","https://openalex.org/W2185687637","https://openalex.org/W2491010324","https://openalex.org/W2503208005","https://openalex.org/W2564031986","https://openalex.org/W2797641211","https://openalex.org/W3122167020","https://openalex.org/W4205992601","https://openalex.org/W4235708440","https://openalex.org/W4247874407","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2324487000","https://openalex.org/W4229457442","https://openalex.org/W1973253908","https://openalex.org/W2060439759","https://openalex.org/W1999074586","https://openalex.org/W2184613118","https://openalex.org/W3215603717","https://openalex.org/W3120703968","https://openalex.org/W2950871635","https://openalex.org/W3126538750"],"abstract_inverted_index":{"We":[0],"numerically":[1],"solve":[2],"parabolic":[3],"problems":[4],"$u_t+\\cA":[5],"u=0$":[6],"in":[7,34,40,48,68,97,116],"$(0,T)\\times\\Omega$,":[8],"$T":[9],"<":[10],"\\infty$,":[11],"where":[12],"$\\Omega\\subset\\mathbb{R}$":[13],"is":[14,20,90],"a":[15,21,37],"bounded":[16],"interval":[17],"and":[18,36,105],"$\\cA$":[19],"strongly":[22],"elliptic":[23],"integrodifferential":[24],"operator":[25],"of":[26,53,87,100,103],"order":[27],"$\\rho\\in[0,2]$.":[28],"A":[29],"discontinuous":[30,112],"Galerkin":[31],"(dG)":[32],"discretization":[33,39],"time":[35,70],"wavelet":[38,62],"space":[41],"are":[42,55,72,118],"used.":[43],"The":[44,65],"densely":[45],"populated":[46],"matrices":[47],"the":[49,85,98],"corresponding":[50],"linear":[51,66,91],"systems":[52,67],"equations":[54],"replaced":[56],"by":[57,74],"sparse":[58],"ones":[59],"using":[60],"appropriate":[61],"compression":[63],"techniques.":[64],"each":[69],"step":[71],"solved":[73],"an":[75],"incomplete":[76],"GMRES":[77],"iteration.":[78],"Under":[79],"these":[80],"conditions,":[81],"we":[82],"show":[83],"that":[84],"complexity":[86],"our":[88],"algorithm":[89],"(up":[92],"to":[93,110],"some":[94],"logarithmic":[95],"terms)":[96],"number":[99],"spatial":[101],"degrees":[102],"freedom":[104],"present":[106],"error":[107],"estimates.":[108],"Applications":[109],"purely":[111],"L\u00e9vy":[113],"processes":[114],"arising":[115],"finance":[117],"given.":[119]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":9}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}