{"id":"https://openalex.org/W4206278804","doi":"https://doi.org/10.1007/s40314-021-01740-y","title":"Linearly implicit local energy-preserving algorithm for a class of multi-symplectic Hamiltonian PDEs","display_name":"Linearly implicit local energy-preserving algorithm for a class of multi-symplectic Hamiltonian PDEs","publication_year":2021,"publication_date":"2021-12-31","ids":{"openalex":"https://openalex.org/W4206278804","doi":"https://doi.org/10.1007/s40314-021-01740-y"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01740-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01740-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5101544552","display_name":"Jiaxiang Cai","orcid":"https://orcid.org/0000-0002-5162-6519"},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]},{"id":"https://openalex.org/I152031979","display_name":"Nanjing Normal University","ror":"https://ror.org/036trcv74","country_code":"CN","type":"education","lineage":["https://openalex.org/I152031979"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiaxiang Cai","raw_affiliation_strings":["School of Geography, Nanjing Normal University, Nanjing, 210023, Jiangsu, China","School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"School of Geography, Nanjing Normal University, Nanjing, 210023, Jiangsu, China","institution_ids":["https://openalex.org/I152031979"]},{"raw_affiliation_string":"School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, Jiangsu, China","institution_ids":["https://openalex.org/I4210147117"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5039042373","display_name":"Bangyu Shen","orcid":"https://orcid.org/0000-0001-6982-0750"},"institutions":[{"id":"https://openalex.org/I4210147117","display_name":"Huaiyin Normal University","ror":"https://ror.org/03xvggv44","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210147117"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Bangyu Shen","raw_affiliation_strings":["School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, Jiangsu, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Huaiyin Normal University, Huaian, 223300, Jiangsu, China","institution_ids":["https://openalex.org/I4210147117"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101544552"],"corresponding_institution_ids":["https://openalex.org/I152031979","https://openalex.org/I4210147117"],"apc_list":null,"apc_paid":null,"fwci":0.9306,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.73903262,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"41","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9962999820709229,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9883000254631042,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.8670452237129211},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8255140781402588},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7535718679428101},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.598494827747345},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.5798872113227844},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.545936107635498},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5238747000694275},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.4925473630428314},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.45275235176086426},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41562968492507935},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3601696491241455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32722559571266174},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.30545610189437866},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.19186639785766602}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8670452237129211},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8255140781402588},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7535718679428101},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.598494827747345},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.5798872113227844},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.545936107635498},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5238747000694275},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.4925473630428314},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.45275235176086426},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41562968492507935},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3601696491241455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32722559571266174},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.30545610189437866},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.19186639785766602}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01740-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01740-y","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.8899999856948853,"id":"https://metadata.un.org/sdg/7","display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G1409181374","display_name":null,"funder_award_id":"2020M671532","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G1885650727","display_name":null,"funder_award_id":"2020Z147","funder_id":"https://openalex.org/F4320313574","funder_display_name":"Jiangsu Province Postdoctoral Science Foundation"},{"id":"https://openalex.org/G6834009548","display_name":null,"funder_award_id":"220","funder_id":"https://openalex.org/F4320327794","funder_display_name":"Qinglan Project of Jiangsu Province of China"}],"funders":[{"id":"https://openalex.org/F4320313574","display_name":"Jiangsu Province Postdoctoral Science Foundation","ror":null},{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320327794","display_name":"Qinglan Project of Jiangsu Province of China","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W1975034694","https://openalex.org/W1976021283","https://openalex.org/W1986208932","https://openalex.org/W2000457254","https://openalex.org/W2002675188","https://openalex.org/W2007263745","https://openalex.org/W2019522628","https://openalex.org/W2023446343","https://openalex.org/W2023558219","https://openalex.org/W2026031976","https://openalex.org/W2044117901","https://openalex.org/W2045019204","https://openalex.org/W2056965879","https://openalex.org/W2061788616","https://openalex.org/W2063604850","https://openalex.org/W2079688335","https://openalex.org/W2086424643","https://openalex.org/W2089285725","https://openalex.org/W2093162681","https://openalex.org/W2121954553","https://openalex.org/W2132119729","https://openalex.org/W2132947916","https://openalex.org/W2475157539","https://openalex.org/W2526298107","https://openalex.org/W2547489428","https://openalex.org/W2883901506","https://openalex.org/W2887352385","https://openalex.org/W2890253154","https://openalex.org/W2907045096","https://openalex.org/W2978703516","https://openalex.org/W3007701048","https://openalex.org/W3092549130","https://openalex.org/W3103494649","https://openalex.org/W3106439850"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2349121885","https://openalex.org/W2360287111","https://openalex.org/W2363725880","https://openalex.org/W2337185636","https://openalex.org/W3149680620","https://openalex.org/W2952286465","https://openalex.org/W2466040413","https://openalex.org/W4298287745","https://openalex.org/W2272143818"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}