{"id":"https://openalex.org/W7166888011","doi":"https://doi.org/10.1007/s10444-026-10325-4","title":"A straightforward discrete energy technique for weighted and shifted backward differentiation formulas up to fifth order","display_name":"A straightforward discrete energy technique for weighted and shifted backward differentiation formulas up to fifth order","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7166888011","doi":"https://doi.org/10.1007/s10444-026-10325-4"},"language":"en","primary_location":{"id":"doi:10.1007/s10444-026-10325-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10325-4","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/A5102301370","display_name":"Yuanyuan Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuanyuan Kang","raw_affiliation_strings":["Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, 411105, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan, 411105, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051810915","display_name":"D. Li","orcid":null},"institutions":[{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dongqian Li","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, Hunan, 411105, China","institution_ids":["https://openalex.org/I4610292"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024865406","display_name":"Yin Yang","orcid":"https://orcid.org/0000-0002-7435-152X"},"institutions":[{"id":"https://openalex.org/I121296143","display_name":"Hunan University of Science and Technology","ror":"https://ror.org/02m9vrb24","country_code":"CN","type":"education","lineage":["https://openalex.org/I121296143"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yin Yang","raw_affiliation_strings":["Hunan Research Center of the Basic Discipline Fundamental Algorithmic Theory and Novel Computational Methods, Xiangtan University, Xiangtan, Hunan, 411105, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Hunan Research Center of the Basic Discipline Fundamental Algorithmic Theory and Novel Computational Methods, Xiangtan University, Xiangtan, Hunan, 411105, China","institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5024865406"],"corresponding_institution_ids":["https://openalex.org/I121296143","https://openalex.org/I4610292"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.66446686,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"52","issue":"4","first_page":null,"last_page":null},"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":0.38359999656677246,"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":0.38359999656677246,"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":0.16670000553131104,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.08789999783039093,"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/multiplier","display_name":"Multiplier (economics)","score":0.6877999901771545},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5336999893188477},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5264999866485596},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.47749999165534973},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.3944000005722046},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.36340001225471497},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.3328000009059906}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8565999865531921},{"id":"https://openalex.org/C124584101","wikidata":"https://www.wikidata.org/wiki/Q1053266","display_name":"Multiplier (economics)","level":2,"score":0.6877999901771545},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5336999893188477},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5264999866485596},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.507099986076355},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.47749999165534973},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.3944000005722046},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3734999895095825},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.36340001225471497},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.3328000009059906},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.31709998846054077},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.28850001096725464},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C55689738","wikidata":"https://www.wikidata.org/wiki/Q15963867","display_name":"Discrete time and continuous time","level":2,"score":0.26080000400543213},{"id":"https://openalex.org/C96314035","wikidata":"https://www.wikidata.org/wiki/Q5282062","display_name":"Discrete system","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10444-026-10325-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10444-026-10325-4","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":[{"score":0.9000276923179626,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[{"id":"https://openalex.org/G8351604488","display_name":null,"funder_award_id":"12571469","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1990730790","https://openalex.org/W1993309344","https://openalex.org/W2000486121","https://openalex.org/W2026646621","https://openalex.org/W2030534447","https://openalex.org/W2147268354","https://openalex.org/W2586273518","https://openalex.org/W3091197941","https://openalex.org/W3127445561","https://openalex.org/W3201152713","https://openalex.org/W4384276752","https://openalex.org/W4387742399","https://openalex.org/W4400599783","https://openalex.org/W4400692988","https://openalex.org/W4401503819","https://openalex.org/W4403468540","https://openalex.org/W4405514329","https://openalex.org/W4410723876"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2026-07-02T00:00:00"}