{"id":"https://openalex.org/W1993309344","doi":"https://doi.org/10.1007/s00211-015-0702-0","title":"Fully implicit, linearly implicit and implicit\u2013explicit backward difference formulae for quasi-linear parabolic equations","display_name":"Fully implicit, linearly implicit and implicit\u2013explicit backward difference formulae for quasi-linear parabolic equations","publication_year":2015,"publication_date":"2015-01-10","ids":{"openalex":"https://openalex.org/W1993309344","doi":"https://doi.org/10.1007/s00211-015-0702-0","mag":"1993309344"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-015-0702-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-015-0702-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","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/A5013053188","display_name":"Georgios Akrivis","orcid":"https://orcid.org/0000-0003-1851-0757"},"institutions":[{"id":"https://openalex.org/I194019607","display_name":"University of Ioannina","ror":"https://ror.org/01qg3j183","country_code":"GR","type":"education","lineage":["https://openalex.org/I194019607"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Georgios Akrivis","raw_affiliation_strings":["Department of Computer Science and Engineering, University of Ioannina, 451\u00a010\u00a0, Ioannina, Greece","Department of Computer Science and Engineering, University of Ioannina, Ioannina, Greece 451 10#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Ioannina, 451\u00a010\u00a0, Ioannina, Greece","institution_ids":["https://openalex.org/I194019607"]},{"raw_affiliation_string":"Department of Computer Science and Engineering, University of Ioannina, Ioannina, Greece 451 10#TAB#","institution_ids":["https://openalex.org/I194019607"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle, 72076\u00a0, T\u00fcbingen, Germany","Mathematisches Institut, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany 72076#TAB#"],"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle, 72076\u00a0, T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, T\u00fcbingen, Germany 72076#TAB#","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5013053188"],"corresponding_institution_ids":["https://openalex.org/I194019607"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":9.0835,"has_fulltext":false,"cited_by_count":72,"citation_normalized_percentile":{"value":0.98358061,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"131","issue":"4","first_page":"713","last_page":"735"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9993000030517578,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9991999864578247,"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":0.9987999796867371,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8948370814323425},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.5887071490287781},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5460290312767029},{"id":"https://openalex.org/keywords/explicit-and-implicit-methods","display_name":"Explicit and implicit methods","score":0.5226737856864929},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5134001970291138},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.5109838247299194},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4461268484592438},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41148611903190613},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.20696711540222168},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.08817040920257568},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.08015140891075134}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8948370814323425},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.5887071490287781},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5460290312767029},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.5226737856864929},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5134001970291138},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.5109838247299194},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4461268484592438},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41148611903190613},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.20696711540222168},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.08817040920257568},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.08015140891075134},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-015-0702-0","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-015-0702-0","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8199999928474426,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W99776242","https://openalex.org/W1509923322","https://openalex.org/W1966401910","https://openalex.org/W1990730790","https://openalex.org/W1995504856","https://openalex.org/W2026646621","https://openalex.org/W2030534447","https://openalex.org/W2037066865","https://openalex.org/W2052045706","https://openalex.org/W2075857446","https://openalex.org/W2078767654","https://openalex.org/W2082621526","https://openalex.org/W2104410771","https://openalex.org/W2110719162","https://openalex.org/W2147268354","https://openalex.org/W2586273518","https://openalex.org/W4234178278","https://openalex.org/W4251840481","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2048226115","https://openalex.org/W4206762967","https://openalex.org/W4229586813","https://openalex.org/W3033917653","https://openalex.org/W1977379644","https://openalex.org/W3091448100","https://openalex.org/W2358336335","https://openalex.org/W1842793358","https://openalex.org/W1926143101","https://openalex.org/W2188177662"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}