{"id":"https://openalex.org/W3121695056","doi":"https://doi.org/10.1007/s10444-020-09839-2","title":"Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations","display_name":"Stability and error estimates for the variable step-size BDF2 method for linear and semilinear parabolic equations","publication_year":2021,"publication_date":"2021-01-21","ids":{"openalex":"https://openalex.org/W3121695056","doi":"https://doi.org/10.1007/s10444-020-09839-2","mag":"3121695056"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-020-09839-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-020-09839-2","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","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/A5014198183","display_name":"Wansheng Wang","orcid":"https://orcid.org/0000-0002-2128-7501"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wansheng Wang","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China"],"raw_orcid":"https://orcid.org/0000-0002-2128-7501","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050568801","display_name":"Mengli Mao","orcid":"https://orcid.org/0000-0003-1410-9624"},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengli Mao","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100401179","display_name":"Zheng Wang","orcid":null},"institutions":[{"id":"https://openalex.org/I21945476","display_name":"Shanghai Normal University","ror":"https://ror.org/01cxqmw89","country_code":"CN","type":"education","lineage":["https://openalex.org/I21945476"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Wang","raw_affiliation_strings":["Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai Normal University, 200234, Shanghai, China","institution_ids":["https://openalex.org/I21945476"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5014198183"],"corresponding_institution_ids":["https://openalex.org/I21945476"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":7.8102,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.98369808,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"47","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9995999932289124,"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":0.9994000196456909,"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":0.9348466396331787},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6797851324081421},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.6411847472190857},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.6242096424102783},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.6212738752365112},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5991058945655823},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5347548723220825},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.5124605298042297},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4467341899871826},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.416882187128067},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.36059239506721497},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.17065361142158508},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.12700659036636353},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.06491875648498535},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.0574517548084259}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9348466396331787},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6797851324081421},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.6411847472190857},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.6242096424102783},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.6212738752365112},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5991058945655823},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5347548723220825},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.5124605298042297},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4467341899871826},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.416882187128067},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.36059239506721497},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.17065361142158508},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.12700659036636353},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.06491875648498535},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.0574517548084259},{"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/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/s10444-020-09839-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-020-09839-2","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"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":"Advances in Computational Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G7972601977","display_name":null,"funder_award_id":"11771060","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1560060148","https://openalex.org/W1968790851","https://openalex.org/W1972154317","https://openalex.org/W1976948879","https://openalex.org/W1983119685","https://openalex.org/W1985723462","https://openalex.org/W1993309344","https://openalex.org/W2012782964","https://openalex.org/W2026110563","https://openalex.org/W2030940697","https://openalex.org/W2041001120","https://openalex.org/W2058080316","https://openalex.org/W2058344980","https://openalex.org/W2073851030","https://openalex.org/W2075872548","https://openalex.org/W2082621526","https://openalex.org/W2090708196","https://openalex.org/W2092013685","https://openalex.org/W2095072225","https://openalex.org/W2115086321","https://openalex.org/W2168568158","https://openalex.org/W2187739482","https://openalex.org/W2575604748","https://openalex.org/W2917228799","https://openalex.org/W2948777523","https://openalex.org/W6602286692","https://openalex.org/W6814092092"],"related_works":["https://openalex.org/W2142285866","https://openalex.org/W2015517699","https://openalex.org/W2281892811","https://openalex.org/W1974047522","https://openalex.org/W3033917653","https://openalex.org/W2048226115","https://openalex.org/W2969796302","https://openalex.org/W4285790117","https://openalex.org/W2975741474","https://openalex.org/W101165111"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":2}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2025-10-10T00:00:00"}