{"id":"https://openalex.org/W2013065","doi":"https://doi.org/10.1007/bf02242919","title":"Asymptotic error expansions for stiff equations: Applications","display_name":"Asymptotic error expansions for stiff equations: Applications","publication_year":1990,"publication_date":"1990-09-01","ids":{"openalex":"https://openalex.org/W2013065","doi":"https://doi.org/10.1007/bf02242919","mag":"2013065"},"language":"en","primary_location":{"id":"doi:10.1007/bf02242919","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02242919","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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/A5078223437","display_name":"Winfried Auzinger","orcid":"https://orcid.org/0000-0002-9631-2601"},"institutions":[{"id":"https://openalex.org/I121760703","display_name":"University of Applied Sciences Technikum Wien","ror":"https://ror.org/04jsx0x49","country_code":"AT","type":"education","lineage":["https://openalex.org/I121760703"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"W. Auzinger","raw_affiliation_strings":["Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","Technische Univ. Wien, Vienna, Austria#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Technische Univ. Wien, Vienna, Austria#TAB#","institution_ids":["https://openalex.org/I121760703"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5078327030","display_name":"Reinhard Frank","orcid":null},"institutions":[{"id":"https://openalex.org/I121760703","display_name":"University of Applied Sciences Technikum Wien","ror":"https://ror.org/04jsx0x49","country_code":"AT","type":"education","lineage":["https://openalex.org/I121760703"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"R. Frank","raw_affiliation_strings":["Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","Technische Univ. Wien, Vienna, Austria#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Technische Univ. Wien, Vienna, Austria#TAB#","institution_ids":["https://openalex.org/I121760703"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089791920","display_name":"G. Kirlinger","orcid":null},"institutions":[{"id":"https://openalex.org/I121760703","display_name":"University of Applied Sciences Technikum Wien","ror":"https://ror.org/04jsx0x49","country_code":"AT","type":"education","lineage":["https://openalex.org/I121760703"]},{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"G. Kirlinger","raw_affiliation_strings":["Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","Technische Univ. Wien, Vienna, Austria#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Angewandte und Numerische Mathematik, Technische Universit\u00e4t Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Technische Univ. Wien, Vienna, Austria#TAB#","institution_ids":["https://openalex.org/I121760703"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2890,"currency":"USD","value_usd":2890},"apc_paid":null,"fwci":0.9524,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.71229862,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"43","issue":"3","first_page":"223","last_page":"253"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9987999796867371,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987999796867371,"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":0.9986000061035156,"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/extrapolation","display_name":"Extrapolation","score":0.794913649559021},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6965662240982056},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6738859415054321},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6554587483406067},{"id":"https://openalex.org/keywords/midpoint-method","display_name":"Midpoint method","score":0.6414639949798584},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6147061586380005},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5707582235336304},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.4962154030799866},{"id":"https://openalex.org/keywords/trapezoidal-rule","display_name":"Trapezoidal rule","score":0.48542389273643494},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4658679962158203},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.45463886857032776},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.453361839056015},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.4357331693172455},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36342912912368774},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.338306188583374},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.21928545832633972}],"concepts":[{"id":"https://openalex.org/C132459708","wikidata":"https://www.wikidata.org/wiki/Q744069","display_name":"Extrapolation","level":2,"score":0.794913649559021},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6965662240982056},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6738859415054321},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6554587483406067},{"id":"https://openalex.org/C85807060","wikidata":"https://www.wikidata.org/wiki/Q17103851","display_name":"Midpoint method","level":2,"score":0.6414639949798584},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6147061586380005},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5707582235336304},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.4962154030799866},{"id":"https://openalex.org/C78727","wikidata":"https://www.wikidata.org/wiki/Q833293","display_name":"Trapezoidal rule","level":3,"score":0.48542389273643494},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4658679962158203},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.45463886857032776},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.453361839056015},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.4357331693172455},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36342912912368774},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.338306188583374},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.21928545832633972},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","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},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bf02242919","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02242919","pdf_url":null,"source":{"id":"https://openalex.org/S35593046","display_name":"Computing","issn_l":"0010-485X","issn":["0010-485X","1436-5057"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"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":8,"referenced_works":["https://openalex.org/W1966233677","https://openalex.org/W1997236034","https://openalex.org/W2051998357","https://openalex.org/W2062990331","https://openalex.org/W2080617060","https://openalex.org/W2083383256","https://openalex.org/W2111719173","https://openalex.org/W4231450125"],"related_works":["https://openalex.org/W2330791370","https://openalex.org/W2063840785","https://openalex.org/W2342494873","https://openalex.org/W2357395917","https://openalex.org/W1966233677","https://openalex.org/W2056024094","https://openalex.org/W2301897886","https://openalex.org/W2089955609","https://openalex.org/W87813395","https://openalex.org/W2013065"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}