{"id":"https://openalex.org/W1969942989","doi":"https://doi.org/10.1137/s0036142901384484","title":"A Predicted Sequential Regularization Method for Index-2 Hessenberg DAEs","display_name":"A Predicted Sequential Regularization Method for Index-2 Hessenberg DAEs","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1969942989","doi":"https://doi.org/10.1137/s0036142901384484","mag":"1969942989"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901384484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384484","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/A5063304710","display_name":"Ping Lin","orcid":"https://orcid.org/0000-0002-4378-7929"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ping Lin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5084076822","display_name":"Raymond J. Spiteri","orcid":"https://orcid.org/0000-0002-3513-6237"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Raymond J. Spiteri","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5063304710"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5209,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.63291925,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"39","issue":"6","first_page":"1889","last_page":"1913"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9973000288009644,"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"}},{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9973000288009644,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7816129922866821},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.6345950365066528},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5389249324798584},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5344570875167847},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4850444197654724},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.47462356090545654},{"id":"https://openalex.org/keywords/extrapolation","display_name":"Extrapolation","score":0.45430123805999756},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.4326445460319519},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3505607843399048},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3333512544631958},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.30085811018943787},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27923405170440674},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.26278847455978394},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14847087860107422}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7816129922866821},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.6345950365066528},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5389249324798584},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5344570875167847},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4850444197654724},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.47462356090545654},{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.45430123805999756},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.4326445460319519},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3505607843399048},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3333512544631958},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.30085811018943787},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27923405170440674},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.26278847455978394},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14847087860107422},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/s0036142901384484","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901384484","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:discovery.dundee.ac.uk:openaire_cris_publications/12bf2b9a-2edd-49da-b140-7241285747c8","is_oa":false,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/12bf2b9a-2edd-49da-b140-7241285747c8","pdf_url":null,"source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lin, P & Spiteri, R J 2002, 'A predicted sequential regularization method for index-2 Hessenberg DAEs', SIAM Journal on Numerical Analysis, vol. 39, no. 6, pp. 1889-1913. < http://www.jstor.org/stable/4101043 >","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:scholarbank.nus.edu.sg:10635/102730","is_oa":false,"landing_page_url":"http://scholarbank.nus.edu.sg/handle/10635/102730","pdf_url":null,"source":{"id":"https://openalex.org/S7407052290","display_name":"National University of Singapore","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scopus","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W202623882","https://openalex.org/W1509997287","https://openalex.org/W1544155718","https://openalex.org/W1554214203","https://openalex.org/W1568666422","https://openalex.org/W1592421646","https://openalex.org/W1597944220","https://openalex.org/W1975537977","https://openalex.org/W1985838247","https://openalex.org/W1991556834","https://openalex.org/W1993835219","https://openalex.org/W1995504856","https://openalex.org/W2000873346","https://openalex.org/W2005470604","https://openalex.org/W2007255973","https://openalex.org/W2023344463","https://openalex.org/W2027726943","https://openalex.org/W2027805119","https://openalex.org/W2028893140","https://openalex.org/W2029323588","https://openalex.org/W2036597275","https://openalex.org/W2039185176","https://openalex.org/W2042561164","https://openalex.org/W2045891213","https://openalex.org/W2047180056","https://openalex.org/W2052888863","https://openalex.org/W2054767684","https://openalex.org/W2075151302","https://openalex.org/W2076000255","https://openalex.org/W2085385512","https://openalex.org/W2087057555","https://openalex.org/W2089424027","https://openalex.org/W2111956410","https://openalex.org/W2140779530","https://openalex.org/W2144144709","https://openalex.org/W2809460247","https://openalex.org/W3209416867","https://openalex.org/W4213104200","https://openalex.org/W4293515545"],"related_works":["https://openalex.org/W1459866636","https://openalex.org/W2566261648","https://openalex.org/W1996574028","https://openalex.org/W1602416982","https://openalex.org/W1990083358","https://openalex.org/W1545187122","https://openalex.org/W2278428637","https://openalex.org/W2088005785","https://openalex.org/W1994850555","https://openalex.org/W797453289"],"abstract_inverted_index":{"The":[0,19],"sequential":[1],"regularization":[2,40],"method":[3,9,77],"(SRM)":[4],"is":[5,32],"a":[6,28,51,88,106,152,160,181,201],"dynamic":[7,81,100],"iterative":[8],"for":[10,110,166,184,216],"the":[11,22,49,60,72,75,94,131,136,144,148,155,167,185,197,204],"numerical":[12,76,127],"solution":[13],"of":[14,24,62,74,96,147,163,171,174],"higher-index":[15],"differential-algebraic":[16],"equations":[17],"(DAEs).":[18],"SRM":[20,50,63,90,156],"has":[21],"advantage":[23],"being":[25],"based":[26,142],"on":[27,143],"regularized":[29],"problem":[30],"that":[31,92,192],"less":[33],"stiff":[34],"than":[35],"those":[36],"produced":[37],"by":[38],"standard":[39],"methods.":[41,176],"Consequently,":[42],"nonstiff":[43],"integrators":[44],"may":[45],"be":[46,68],"used,":[47],"making":[48],"competitive":[52],"alternative":[53],"to":[54,67,71,102,115,129],"popular":[55],"integrators.":[56],"In":[57,83,177],"past":[58],"work,":[59],"number":[61,95],"iterations":[64,97],"was":[65],"taken":[66],"roughly":[69],"equal":[70],"order":[73,194],"used":[78],"in":[79,98,196],"each":[80,99],"iteration.":[82],"this":[84],"paper,":[85],"we":[86,179],"propose":[87],"predicted":[89,132],"(PSRM)":[91],"reduces":[93],"iteration":[101,157],"one.":[103],"We":[104,124],"give":[105,126,180],"new":[107,207],"error":[108],"analysis":[109],"explicit":[111],"Runge--Kutta":[112,175],"methods":[113,141],"applied":[114],"linear":[116],"index-2":[117],"Hessenberg":[118],"DAEs":[119,149],"with":[120],"or":[121],"without":[122],"singularities.":[123],"also":[125],"examples":[128],"confirm":[130],"convergence":[133,214],"rates.":[134],"For":[135],"PSRM,":[137],"extrapolation":[138],"formulas":[139],"and":[140,154,212],"differential":[145,198],"part":[146],"serve":[150],"as":[151,159],"predictor,":[153],"serves":[158],"corrector.":[161],"Implementation":[162],"higher-order":[164],"schemes":[165],"PSRM":[168],"makes":[169],"use":[170],"continuous":[172],"extensions":[173],"particular,":[178],"prediction":[182],"scheme":[183],"algebraic":[186],"variable":[187,199],"at":[188],"intermediate":[189],"stage":[190],"points":[191],"suppresses":[193],"reduction":[195],"near":[200],"singularity.":[202],"Moreover,":[203],"SRM/PSRM":[205],"provides":[206],"insight":[208],"into":[209],"operator":[210],"splitting":[211],"fast":[213],"rates":[215],"waveform":[217],"relaxation.":[218]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}