{"id":"https://openalex.org/W2136838269","doi":"https://doi.org/10.1137/s1064827598349057","title":"Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations","display_name":"Index Concepts for Linear Mixed Systems of Differential-Algebraic and Hyperbolic-Type Equations","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W2136838269","doi":"https://doi.org/10.1137/s1064827598349057","mag":"2136838269"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827598349057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598349057","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080524539","display_name":"Michael G\u00fcnther","orcid":"https://orcid.org/0000-0002-2195-4300"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael G\u00fcnther","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5028123504","display_name":"Yvonne Wagner","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yvonne Wagner","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080524539"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.9603,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.90657084,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"5","first_page":"1610","last_page":"1629"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994000196456909,"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/T13286","display_name":"Modeling and Simulation Systems","score":0.9962999820709229,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9933000206947327,"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":0.8478671312332153},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6118728518486023},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5466405153274536},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5323125720024109},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5020627975463867},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.49863266944885254},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4752975404262543},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47051873803138733},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4658207893371582},{"id":"https://openalex.org/keywords/algebraic-equation","display_name":"Algebraic equation","score":0.46461808681488037},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.447254478931427},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4288583993911743},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.1994408667087555}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8478671312332153},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6118728518486023},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5466405153274536},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5323125720024109},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5020627975463867},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.49863266944885254},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4752975404262543},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47051873803138733},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4658207893371582},{"id":"https://openalex.org/C23917780","wikidata":"https://www.wikidata.org/wiki/Q50698","display_name":"Algebraic equation","level":3,"score":0.46461808681488037},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.447254478931427},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4288583993911743},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.1994408667087555},{"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/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827598349057","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827598349057","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:tubiblio.ulb.tu-darmstadt.de:9329","is_oa":false,"landing_page_url":"http://tubiblio.ulb.tu-darmstadt.de/view/person/G=FCnther=3AMichael=3A=3A.html>","pdf_url":null,"source":{"id":"https://openalex.org/S4377196390","display_name":"TUbilio (Technical University of Darmstadt)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I31512782","host_organization_name":"Technische Universit\u00e4t Darmstadt","host_organization_lineage":["https://openalex.org/I31512782"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":null,"raw_type":"PeerReviewed"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W63458695","https://openalex.org/W1509702815","https://openalex.org/W1509923322","https://openalex.org/W1592421646","https://openalex.org/W1651707596","https://openalex.org/W1967011851","https://openalex.org/W1973008872","https://openalex.org/W1974203503","https://openalex.org/W1983438352","https://openalex.org/W1995504856","https://openalex.org/W2009573643","https://openalex.org/W2017402786","https://openalex.org/W2023799049","https://openalex.org/W2050471685","https://openalex.org/W2060580374","https://openalex.org/W2075151302","https://openalex.org/W2075278368","https://openalex.org/W2076751185","https://openalex.org/W2104427203","https://openalex.org/W2497141301","https://openalex.org/W3111685920","https://openalex.org/W4251707447","https://openalex.org/W4285719527","https://openalex.org/W4292079189"],"related_works":["https://openalex.org/W2999616507","https://openalex.org/W3164276969","https://openalex.org/W2049253768","https://openalex.org/W2023803998","https://openalex.org/W2107705030","https://openalex.org/W3021188244","https://openalex.org/W2122287774","https://openalex.org/W2278010680","https://openalex.org/W2321083928","https://openalex.org/W1511803145"],"abstract_inverted_index":{"For":[0],"many":[1],"technical":[2],"systems,":[3,58],"the":[4,38,42,80,83,90,94,100,104,143,148,151,171,176,180],"use":[5],"of":[6,18,26,82,93,103,118,132,150],"a":[7,115,127,130],"refined":[8],"network":[9,43],"modeling":[10],"approach":[11],"leads":[12],"to":[13,55,69,86,112,167],"hyperbolic-type":[14],"initial-boundary":[15],"value":[16],"problems":[17],"partial":[19],"differential-algebraic":[20,33],"equations":[21,34],"(PDAEs).":[22],"The":[23],"boundary":[24],"conditions":[25],"these":[27,57,158],"systems":[28,106,145],"are":[29,46],"governed":[30],"by":[31,48],"time-dependent":[32],"(DAEs)":[35],"that":[36,45,64,78,157],"couple":[37],"PDAE":[39],"system":[40,85],"with":[41,165],"elements":[44],"modeled":[47],"DAEs":[49],"in":[50,89,99,120,141],"time":[51],"only.":[52],"In":[53,110],"order":[54,111],"classify":[56],"we":[59,124],"extend":[60],"some":[61],"index":[62,75],"notions":[63],"have":[65],"already":[66],"been":[67],"introduced":[68],"treat":[70],"parabolic-type":[71],"problems.":[72],"A":[73],"perturbation":[74],"is":[76,138],"considered":[77],"reflects":[79],"sensitivity":[81,164],"mixed":[84],"slight":[87],"perturbations":[88],"right-hand":[91],"side":[92],"PDAEs,":[95],"as":[96,98],"well":[97],"input":[101],"signals":[102],"DAE":[105],"and":[107,122,129],"initial":[108],"values.":[109],"make":[113],"an":[114,162],"posteriori":[116],"analysis":[117],"semidiscretization":[119,172],"space":[121,128],"time,":[123],"introduce":[125],"additionally":[126],"method":[131],"lines":[133],"(MOL)":[134],"index.":[135],"Here":[136],"one":[137],"especially":[139],"interested":[140],"whether":[142],"semidiscretized":[144],"properly":[146],"reflect":[147],"properties":[149],"underlying":[152],"systems.":[153],"We":[154],"will":[155],"show":[156],"indices":[159],"may":[160],"detect":[161],"artificial":[163],"respect":[166],"perturbations,":[168],"e.g.,":[169],"if":[170],"does":[173],"not":[174],"consider":[175],"information":[177],"transport":[178],"along":[179],"characteristics.":[181]},"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
