{"id":"https://openalex.org/W2079635391","doi":"https://doi.org/10.1137/050638886","title":"Variational Methods for Solving Warped Multirate Partial Differential Algebraic Equations","display_name":"Variational Methods for Solving Warped Multirate Partial Differential Algebraic Equations","publication_year":2008,"publication_date":"2008-11-26","ids":{"openalex":"https://openalex.org/W2079635391","doi":"https://doi.org/10.1137/050638886","mag":"2079635391"},"language":"en","primary_location":{"id":"doi:10.1137/050638886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638886","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/A5022413371","display_name":"Roland Pulch","orcid":"https://orcid.org/0000-0002-6503-3300"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Roland Pulch","raw_affiliation_strings":["pulch@math.uni-wuppertal.de#TAB#"],"affiliations":[{"raw_affiliation_string":"pulch@math.uni-wuppertal.de#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022413371"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.09068552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"31","issue":"2","first_page":"1016","last_page":"1034"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9890999794006348,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9890999794006348,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9825999736785889,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9772999882698059,"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/decoupling","display_name":"Decoupling (probability)","score":0.7228509187698364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7115178108215332},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.6202380061149597},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5697308778762817},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5308421850204468},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5255652666091919},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.48362839221954346},{"id":"https://openalex.org/keywords/multivariable-calculus","display_name":"Multivariable calculus","score":0.44791752099990845},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.43061962723731995},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.4110843241214752},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38230717182159424},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28414031863212585},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.12898138165473938}],"concepts":[{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.7228509187698364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7115178108215332},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.6202380061149597},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5697308778762817},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5308421850204468},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5255652666091919},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.48362839221954346},{"id":"https://openalex.org/C117312493","wikidata":"https://www.wikidata.org/wiki/Q2035437","display_name":"Multivariable calculus","level":2,"score":0.44791752099990845},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.43061962723731995},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.4110843241214752},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38230717182159424},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28414031863212585},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.12898138165473938},{"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C133731056","wikidata":"https://www.wikidata.org/wiki/Q4917288","display_name":"Control engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/050638886","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050638886","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":5,"referenced_works":["https://openalex.org/W1605860323","https://openalex.org/W2045519838","https://openalex.org/W2097463278","https://openalex.org/W2112369634","https://openalex.org/W2145320787"],"related_works":["https://openalex.org/W4235120361","https://openalex.org/W2047526305","https://openalex.org/W2162049291","https://openalex.org/W2390964127","https://openalex.org/W2061441219","https://openalex.org/W2382128874","https://openalex.org/W2392975328","https://openalex.org/W2083230593","https://openalex.org/W3189146492","https://openalex.org/W2377697441"],"abstract_inverted_index":{"Signals":[0],"exhibiting":[1],"amplitude":[2],"as":[3,5],"well":[4],"frequency":[6,16,62],"modulation":[7],"at":[8],"widely":[9],"separated":[10],"time":[11,29],"scales":[12,30],"arise":[13],"in":[14,78,126],"radio":[15],"(RF)":[17],"applications.":[18],"A":[19],"multivariate":[20,80],"model":[21],"yields":[22],"an":[23,59,118,144],"adequate":[24],"representation":[25],"by":[26],"decoupling":[27],"the":[28,43,67,79,83,92,130,134,140],"of":[31,37,50,58,69,94,117,133,147],"involved":[32],"signals.":[33,149],"Consequently,":[34],"a":[35,48,106,110,115],"system":[36,49],"differential":[38,52],"algebraic":[39,53],"equations":[40,54],"(DAEs)":[41],"modeling":[42],"electric":[44],"circuit":[45],"changes":[46],"into":[47],"partial":[51,95],"(PDAEs).":[55],"The":[56],"determination":[57],"emerging":[60],"local":[61],"function":[63],"is":[64,85],"crucial":[65],"for":[66,109],"efficiency":[68],"this":[70,98],"approach,":[71],"since":[72],"inappropriate":[73],"choices":[74],"produce":[75],"many":[76],"oscillations":[77],"solution.":[81],"Thus,":[82],"idea":[84],"to":[86,104],"reduce":[87],"oscillating":[88],"behavior":[89],"via":[90],"minimizing":[91],"magnitude":[93],"derivatives.":[96],"For":[97],"purpose,":[99],"we":[100],"apply":[101],"variational":[102],"calculus":[103],"obtain":[105],"necessary":[107],"condition":[108,122],"specific":[111],"solution,":[112],"which":[113],"represents":[114],"minimum":[116],"according":[119],"functional.":[120],"This":[121],"can":[123],"be":[124],"included":[125],"numerical":[127],"schemes":[128],"computing":[129],"complete":[131],"solution":[132],"PDAE.":[135],"Test":[136],"results":[137],"confirm":[138],"that":[139],"used":[141],"strategy":[142],"ensures":[143],"efficient":[145],"simulation":[146],"RF":[148]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
