{"id":"https://openalex.org/W2167797477","doi":"https://doi.org/10.1109/tcad.2009.2024712","title":"$A$-Stable and $L$-Stable High-Order Integration Methods for Solving Stiff Differential Equations","display_name":"$A$-Stable and $L$-Stable High-Order Integration Methods for Solving Stiff Differential Equations","publication_year":2009,"publication_date":"2009-08-24","ids":{"openalex":"https://openalex.org/W2167797477","doi":"https://doi.org/10.1109/tcad.2009.2024712","mag":"2167797477"},"language":"en","primary_location":{"id":"doi:10.1109/tcad.2009.2024712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2009.2024712","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","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/A5056274353","display_name":"Emad Gad","orcid":"https://orcid.org/0000-0003-4801-3110"},"institutions":[{"id":"https://openalex.org/I153718931","display_name":"University of Ottawa","ror":"https://ror.org/03c4mmv16","country_code":"CA","type":"education","lineage":["https://openalex.org/I153718931"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"E. Gad","raw_affiliation_strings":["School of Information Technology and Engineering, University of Ottawa, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Technology and Engineering, University of Ottawa, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I153718931"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028462988","display_name":"M. Nakhla","orcid":"https://orcid.org/0000-0001-8327-0396"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"M. Nakhla","raw_affiliation_strings":["Department of Electronics, Carleton University, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Carleton University, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084488994","display_name":"Ramachandra Achar","orcid":"https://orcid.org/0000-0002-2822-3674"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"R. Achar","raw_affiliation_strings":["Department of Electronics, Carleton University, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Carleton University, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I67031392"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015367369","display_name":"Yinghong Zhou","orcid":"https://orcid.org/0009-0006-0692-2606"},"institutions":[{"id":"https://openalex.org/I67031392","display_name":"Carleton University","ror":"https://ror.org/02qtvee93","country_code":"CA","type":"education","lineage":["https://openalex.org/I67031392"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yinghong Zhou","raw_affiliation_strings":["Department of Electronics, Carleton University, Ottawa, ONT, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics, Carleton University, Ottawa, ONT, Canada","institution_ids":["https://openalex.org/I67031392"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7648,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.93355019,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"28","issue":"9","first_page":"1359","last_page":"1372"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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":0.9988999962806702,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10187","display_name":"Radio Frequency Integrated Circuit Design","score":0.9959999918937683,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/notation","display_name":"Notation","score":0.7893431186676025},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.552493691444397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4869474172592163},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.47493842244148254},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4596822261810303},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.45781034231185913},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4425998032093048},{"id":"https://openalex.org/keywords/transient","display_name":"Transient (computer programming)","score":0.4357927143573761},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.4141491949558258},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4114450216293335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.407479852437973},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3348967730998993},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18679854273796082},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18040329217910767},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.16451212763786316},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.08748596906661987}],"concepts":[{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.7893431186676025},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.552493691444397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4869474172592163},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.47493842244148254},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4596822261810303},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.45781034231185913},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4425998032093048},{"id":"https://openalex.org/C2780799671","wikidata":"https://www.wikidata.org/wiki/Q17087362","display_name":"Transient (computer programming)","level":2,"score":0.4357927143573761},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.4141491949558258},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4114450216293335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.407479852437973},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3348967730998993},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18679854273796082},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18040329217910767},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.16451212763786316},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.08748596906661987},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tcad.2009.2024712","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tcad.2009.2024712","pdf_url":null,"source":{"id":"https://openalex.org/S100835903","display_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","issn_l":"0278-0070","issn":["0278-0070","1937-4151"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1524305136","https://openalex.org/W1543750907","https://openalex.org/W1585773866","https://openalex.org/W1589971708","https://openalex.org/W1964070472","https://openalex.org/W1981846792","https://openalex.org/W1993409158","https://openalex.org/W1994615638","https://openalex.org/W2004759358","https://openalex.org/W2023344463","https://openalex.org/W2023422324","https://openalex.org/W2034984492","https://openalex.org/W2050296550","https://openalex.org/W2053788580","https://openalex.org/W2090963365","https://openalex.org/W2091967202","https://openalex.org/W2097913753","https://openalex.org/W2098291399","https://openalex.org/W2103086012","https://openalex.org/W2139030761","https://openalex.org/W2142202849","https://openalex.org/W2143145013","https://openalex.org/W2151807147","https://openalex.org/W2166122264","https://openalex.org/W2171886636","https://openalex.org/W2319973481","https://openalex.org/W2478091498","https://openalex.org/W2484971506","https://openalex.org/W3100524519","https://openalex.org/W3203011645","https://openalex.org/W3216945531","https://openalex.org/W4232702608","https://openalex.org/W4249817611","https://openalex.org/W4285719527","https://openalex.org/W4299512035","https://openalex.org/W6680641309"],"related_works":["https://openalex.org/W2504004674","https://openalex.org/W1595229445","https://openalex.org/W2498744856","https://openalex.org/W4390482104","https://openalex.org/W322408318","https://openalex.org/W149041114","https://openalex.org/W2963177394","https://openalex.org/W1965815883","https://openalex.org/W763418848","https://openalex.org/W2024638892"],"abstract_inverted_index":{"<para":[0],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[1],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[2],"This":[3],"paper":[4],"describes":[5],"a":[6],"new":[7,51],"<formula":[8,12,46,92],"formulatype=\"inline\"><tex":[9,13,47,93],"Notation=\"TeX\">$A$</tex></formula>-":[10],"and":[11,110],"Notation=\"TeX\">$L$</tex></formula>-stable":[14,94],"integration":[15,60],"method":[16,52,86],"for":[17,54,62],"simulating":[18],"the":[19,33,45,55,63,79],"time-domain":[20],"transient":[21,64],"response":[22],"of":[23,39,57,66],"nonlinear":[24],"circuits.":[25],"The":[26,50,85],"proposed":[27],"method,":[28],"which":[29],"is":[30],"based":[31],"on":[32],"Obreshkov":[34],"formula,":[35],"can":[36,87],"be":[37,88],"made":[38],"arbitrary":[40],"high":[41],"order":[42,59],"while":[43,69],"maintaining":[44],"Notation=\"TeX\">$A$</tex></formula>-stability":[48],"property.":[49],"allows":[53],"adoption":[56],"higher":[58],"methods":[61],"analysis":[65],"electronic":[67],"circuits":[68,98],"enabling":[70],"them":[71],"to":[72,82,96],"take":[73],"larger":[74],"step":[75],"sizes":[76],"without":[77],"violating":[78],"stability,":[80],"leading":[81],"faster":[83],"simulations.":[84],"run":[89],"in":[90],"an":[91],"mode":[95],"handle":[97],"with":[99],"extremely":[100],"stiff":[101],"equations.":[102],"Necessary":[103],"theoretical":[104],"foundations,":[105],"implementation":[106],"details,":[107],"error-control":[108],"mechanisms,":[109],"computational":[111],"results":[112],"are":[113],"presented.":[114],"</para>":[115]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":7},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
