{"id":"https://openalex.org/W2167891434","doi":"https://doi.org/10.1137/140974833","title":"High-Order Compact Schemes for Parabolic Problems with Mixed Derivatives in Multiple Space Dimensions","display_name":"High-Order Compact Schemes for Parabolic Problems with Mixed Derivatives in Multiple Space Dimensions","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2167891434","doi":"https://doi.org/10.1137/140974833","mag":"2167891434"},"language":"en","primary_location":{"id":"doi:10.1137/140974833","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974833","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1506.06711","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Bertram D\u00fcring","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Bertram D\u00fcring","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Christof Heuer","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christof Heuer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.875,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.97339333,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"53","issue":"5","first_page":"2113","last_page":"2134"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9359999895095825,"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":0.9359999895095825,"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/T10940","display_name":"Navier-Stokes equation solutions","score":0.011099999770522118,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6887999773025513},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6256999969482422},{"id":"https://openalex.org/keywords/compact-finite-difference","display_name":"Compact finite difference","score":0.5769000053405762},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5708000063896179},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5529000163078308},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.492900013923645},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4487999975681305},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.4307999908924103},{"id":"https://openalex.org/keywords/compact-space","display_name":"Compact space","score":0.3937999904155731},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.3840000033378601}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8702999949455261},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6887999773025513},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6256999969482422},{"id":"https://openalex.org/C2780829570","wikidata":"https://www.wikidata.org/wiki/Q25113057","display_name":"Compact finite difference","level":3,"score":0.5769000053405762},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5708000063896179},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5529000163078308},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5449000000953674},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.492900013923645},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4487999975681305},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C18648836","wikidata":"https://www.wikidata.org/wiki/Q381892","display_name":"Compact space","level":2,"score":0.3937999904155731},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.39259999990463257},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.3840000033378601},{"id":"https://openalex.org/C153635880","wikidata":"https://www.wikidata.org/wiki/Q1412436","display_name":"Cauchy problem","level":3,"score":0.3833000063896179},{"id":"https://openalex.org/C54067925","wikidata":"https://www.wikidata.org/wiki/Q3607962","display_name":"Elliptic partial differential equation","level":3,"score":0.3553999960422516},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3537999987602234},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.35269999504089355},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.34389999508857727},{"id":"https://openalex.org/C49344536","wikidata":"https://www.wikidata.org/wiki/Q726441","display_name":"Cauchy distribution","level":2,"score":0.3312000036239624},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.33090001344680786},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.30709999799728394},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.29649999737739563},{"id":"https://openalex.org/C136798861","wikidata":"https://www.wikidata.org/wiki/Q1826712","display_name":"Method of lines","level":5,"score":0.2890999913215637},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.2858999967575073},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.2786000072956085},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.2766999900341034},{"id":"https://openalex.org/C89397928","wikidata":"https://www.wikidata.org/wiki/Q1630320","display_name":"Unconditional convergence","level":5,"score":0.2660999894142151},{"id":"https://openalex.org/C143170015","wikidata":"https://www.wikidata.org/wiki/Q17007850","display_name":"Stability conditions","level":3,"score":0.2563000023365021},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.2549999952316284},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2547999918460846},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.25130000710487366}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/140974833","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140974833","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:arXiv.org:1506.06711","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.06711","pdf_url":"https://arxiv.org/pdf/1506.06711","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1506.06711","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1506.06711","pdf_url":"https://arxiv.org/pdf/1506.06711","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W79980520","https://openalex.org/W1971828511","https://openalex.org/W1985037379","https://openalex.org/W1998788695","https://openalex.org/W2003544057","https://openalex.org/W2033516351","https://openalex.org/W2047384008","https://openalex.org/W2060296485","https://openalex.org/W2068896849","https://openalex.org/W2076443122","https://openalex.org/W2102583609","https://openalex.org/W2103606462","https://openalex.org/W2109252891","https://openalex.org/W2118841251","https://openalex.org/W2119671975","https://openalex.org/W2128387129","https://openalex.org/W2321324753","https://openalex.org/W3121209513"],"related_works":[],"abstract_inverted_index":{"We":[0,46],"present":[1],"a":[2,9,58,76],"high-order":[3,59,168],"compact":[4,60],"finite":[5],"difference":[6],"approach":[7],"for":[8,92,102,133],"class":[10],"of":[11,34,82,111,122,144,153,170,173],"parabolic":[12],"partial":[13,100],"differential":[14],"equations":[15],"with":[16,24],"time-":[17],"and":[18,43,68,88,97,135,156],"space-dependent":[19],"coefficients":[20,52],"as":[21,23],"well":[22],"mixed":[25,94],"second-order":[26,69],"derivative":[27,95],"terms":[28],"in":[29,39,66,71,86,128],"$n$":[30],"spatial":[31,90],"dimensions.":[32],"Problems":[33],"this":[35],"type":[36],"arise":[37],"frequently":[38],"computational":[40,44],"fluid":[41],"dynamics":[42],"finance.":[45],"derive":[47],"general":[48,104],"conditions":[49,147],"on":[50],"the":[51,83,103,112,120,129,141,150,171,174,178],"which":[53,62],"allow":[54],"us":[55],"to":[56,140,166,177],"obtain":[57],"scheme":[61],"is":[63],"fourth-order":[64],"accurate":[65,70],"space":[67],"time.":[72],"Moreover,":[73],"we":[74,118,148],"perform":[75],"thorough":[77],"von":[78],"Neumann":[79],"stability":[80,110],"analysis":[81],"Cauchy":[84],"problem":[85,176],"two":[87,134],"three":[89,136],"dimensions":[91],"vanishing":[93],"terms,":[96],"also":[98],"give":[99],"results":[101,107],"case.":[105],"The":[106],"suggest":[108],"unconditional":[109],"scheme.":[113],"As":[114],"an":[115],"application":[116],"example":[117],"consider":[119],"pricing":[121],"European":[123],"power":[124],"put":[125],"basket":[126],"options":[127],"multidimensional":[130],"Black--Scholes":[131],"model":[132],"underlying":[137],"assets.":[138],"Due":[139],"low":[142],"regularity":[143],"typical":[145],"initial":[146],"employ":[149],"smoothing":[151],"operators":[152],"Kreiss,":[154],"Thomee,":[155],"Widlund":[157],"[Comm.":[158],"Pure":[159],"Appl.":[160],"Math.,":[161],"23":[162],"(1970),":[163],"pp.":[164],"241--259]":[165],"ensure":[167],"convergence":[169],"approximations":[172],"smoothed":[175],"true":[179],"solution.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":8},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2016-06-24T00:00:00"}
