{"id":"https://openalex.org/W1968659814","doi":"https://doi.org/10.1137/s0036142998339921","title":"Space-Time Discretization of Series Expansion Methods for the Boltzmann Transport Equation","display_name":"Space-Time Discretization of Series Expansion Methods for the Boltzmann Transport Equation","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W1968659814","doi":"https://doi.org/10.1137/s0036142998339921","mag":"1968659814"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142998339921","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998339921","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/A5110032299","display_name":"Christian Ringhofer","orcid":null},"institutions":[{"id":"https://openalex.org/I4210152479","display_name":"Statistical Service","ror":"https://ror.org/05vydvf11","country_code":"CY","type":"government","lineage":["https://openalex.org/I4210152479"]}],"countries":["CY"],"is_corresponding":true,"raw_author_name":"Christian Ringhofer","raw_affiliation_strings":["CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)"],"affiliations":[{"raw_affiliation_string":"CLAS-NS: Mathematics and Statistical Sciences, School of (SMSS)","institution_ids":["https://openalex.org/I4210152479"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110032299"],"corresponding_institution_ids":["https://openalex.org/I4210152479"],"apc_list":null,"apc_paid":null,"fwci":3.3846,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.90909091,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"38","issue":"2","first_page":"442","last_page":"465"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9998000264167786,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7209337949752808},{"id":"https://openalex.org/keywords/boltzmann-equation","display_name":"Boltzmann equation","score":0.7175458073616028},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6758989095687866},{"id":"https://openalex.org/keywords/knudsen-number","display_name":"Knudsen number","score":0.6662862300872803},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6056573390960693},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.4647957682609558},{"id":"https://openalex.org/keywords/convection\u2013diffusion-equation","display_name":"Convection\u2013diffusion equation","score":0.46455615758895874},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.45041322708129883},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.41931724548339844},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4147884249687195},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32045215368270874},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19675973057746887},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.1689225435256958},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.11360308527946472}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7209337949752808},{"id":"https://openalex.org/C165995430","wikidata":"https://www.wikidata.org/wiki/Q891653","display_name":"Boltzmann equation","level":2,"score":0.7175458073616028},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6758989095687866},{"id":"https://openalex.org/C121838276","wikidata":"https://www.wikidata.org/wiki/Q898463","display_name":"Knudsen number","level":2,"score":0.6662862300872803},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6056573390960693},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.4647957682609558},{"id":"https://openalex.org/C17456955","wikidata":"https://www.wikidata.org/wiki/Q343279","display_name":"Convection\u2013diffusion equation","level":2,"score":0.46455615758895874},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.45041322708129883},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.41931724548339844},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4147884249687195},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32045215368270874},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19675973057746887},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.1689225435256958},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.11360308527946472},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/s0036142998339921","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142998339921","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":[{"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy","score":0.5199999809265137}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1808002509","https://openalex.org/W1987854780","https://openalex.org/W1995106080","https://openalex.org/W2005010735","https://openalex.org/W2016870785","https://openalex.org/W2051247278","https://openalex.org/W2055380691","https://openalex.org/W2058014884","https://openalex.org/W2060428133","https://openalex.org/W2075807176","https://openalex.org/W2093012458","https://openalex.org/W2610542513","https://openalex.org/W2819436012","https://openalex.org/W3206166500"],"related_works":["https://openalex.org/W2055696851","https://openalex.org/W1484951500","https://openalex.org/W2346735408","https://openalex.org/W109797150","https://openalex.org/W2094595006","https://openalex.org/W2020425962","https://openalex.org/W2017523941","https://openalex.org/W2122862228","https://openalex.org/W3010340598","https://openalex.org/W2469447765"],"abstract_inverted_index":{"The":[0],"approximate":[1],"solution":[2],"of":[3,17,55,69,80,121,124],"the":[4,27,37,53,58,81,88,102,115,122,125],"Boltzmann":[5],"transport":[6],"equation":[7],"via":[8],"Galerkin-type":[9],"series":[10],"expansion":[11,28],"methods":[12,71,100],"leads":[13],"to":[14,36,52],"a":[15,47,67,78],"system":[16,31],"first":[18],"order":[19],"differential":[20],"equations":[21],"in":[22],"space":[23],"and":[24,45,74,118],"time":[25,103],"for":[26,87,101],"coefficients.":[29],"This":[30],"is":[32,72,92],"extremely":[33],"stiff":[34],"close":[35],"fluid":[38],"dynamical":[39],"regime":[40],"(for":[41],"small":[42],"Knudsen":[43,116],"numbers),":[44],"exhibits":[46],"mildly":[48,112],"dispersive":[49],"behavior,":[50],"due":[51],"acceleration":[54],"waves":[56],"by":[57,95],"external":[59],"force":[60],"(the":[61],"electric":[62,126],"field).":[63],"In":[64],"this":[65],"paper":[66],"class":[68],"difference":[70],"presented":[73],"analyzed":[75],"which":[76,109],"represent":[77],"generalization":[79],"well-known":[82],"Scharfetter--Gummel":[83],"exponential":[84],"fitting":[85],"approach":[86],"drift-diffusion":[89],"equations.":[90],"It":[91],"shown":[93],"that,":[94],"using":[96],"appropriate":[97],"operator":[98],"splitting":[99],"discretization,":[104],"one":[105],"obtains":[106],"stability":[107],"properties":[108],"are":[110],"only":[111],"dependent":[113],"on":[114],"number":[117],"essentially":[119],"independent":[120],"size":[123],"field.":[127]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}