{"id":"https://openalex.org/W4378229161","doi":"https://doi.org/10.3390/sym15061146","title":"Explicit K-Symplectic and Symplectic-like Methods for Charged Particle System in General Magnetic Field","display_name":"Explicit K-Symplectic and Symplectic-like Methods for Charged Particle System in General Magnetic Field","publication_year":2023,"publication_date":"2023-05-25","ids":{"openalex":"https://openalex.org/W4378229161","doi":"https://doi.org/10.3390/sym15061146"},"language":"en","primary_location":{"id":"doi:10.3390/sym15061146","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15061146","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1146/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/6/1146/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101206272","display_name":"Yulan Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yulan Lu","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112923074","display_name":"Junbin Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junbin Yuan","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102516417","display_name":"Haoyang Tian","orcid":null},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haoyang Tian","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102516418","display_name":"Zhengwei Qin","orcid":null},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengwei Qin","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100429250","display_name":"Siyuan Chen","orcid":"https://orcid.org/0009-0001-8475-0305"},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Siyuan Chen","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112923075","display_name":"Hongji Zhou","orcid":null},"institutions":[{"id":"https://openalex.org/I92403157","display_name":"University of Science and Technology Beijing","ror":"https://ror.org/02egmk993","country_code":"CN","type":"education","lineage":["https://openalex.org/I92403157"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongji Zhou","raw_affiliation_strings":["School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China","institution_ids":["https://openalex.org/I92403157"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5101206272"],"corresponding_institution_ids":["https://openalex.org/I92403157"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3885,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.50925926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"15","issue":"6","first_page":"1146","last_page":"1146"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9983000159263611,"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/symplectic-geometry","display_name":"Symplectic geometry","score":0.8888401985168457},{"id":"https://openalex.org/keywords/symplectic-matrix","display_name":"Symplectic matrix","score":0.6490986943244934},{"id":"https://openalex.org/keywords/symplectic-representation","display_name":"Symplectic representation","score":0.6225075125694275},{"id":"https://openalex.org/keywords/symplectic-vector-space","display_name":"Symplectic vector space","score":0.5967439413070679},{"id":"https://openalex.org/keywords/symplectic-group","display_name":"Symplectic group","score":0.5824984312057495},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.5353992581367493},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.5208435654640198},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.513340175151825},{"id":"https://openalex.org/keywords/symplectomorphism","display_name":"Symplectomorphism","score":0.5125800967216492},{"id":"https://openalex.org/keywords/phase-space","display_name":"Phase space","score":0.4639987349510193},{"id":"https://openalex.org/keywords/moment-map","display_name":"Moment map","score":0.4390808939933777},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.4366018772125244},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4351559579372406},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.37195566296577454},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3591391444206238},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.30877983570098877},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.15284273028373718},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.07649314403533936}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8888401985168457},{"id":"https://openalex.org/C185535465","wikidata":"https://www.wikidata.org/wiki/Q2705070","display_name":"Symplectic matrix","level":5,"score":0.6490986943244934},{"id":"https://openalex.org/C104586451","wikidata":"https://www.wikidata.org/wiki/Q771008","display_name":"Symplectic representation","level":4,"score":0.6225075125694275},{"id":"https://openalex.org/C125849494","wikidata":"https://www.wikidata.org/wiki/Q766774","display_name":"Symplectic vector space","level":5,"score":0.5967439413070679},{"id":"https://openalex.org/C175322374","wikidata":"https://www.wikidata.org/wiki/Q936434","display_name":"Symplectic group","level":3,"score":0.5824984312057495},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.5353992581367493},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.5208435654640198},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.513340175151825},{"id":"https://openalex.org/C135661100","wikidata":"https://www.wikidata.org/wiki/Q1049064","display_name":"Symplectomorphism","level":3,"score":0.5125800967216492},{"id":"https://openalex.org/C151342819","wikidata":"https://www.wikidata.org/wiki/Q62542","display_name":"Phase space","level":2,"score":0.4639987349510193},{"id":"https://openalex.org/C40265840","wikidata":"https://www.wikidata.org/wiki/Q6897118","display_name":"Moment map","level":3,"score":0.4390808939933777},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.4366018772125244},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4351559579372406},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.37195566296577454},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3591391444206238},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.30877983570098877},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.15284273028373718},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.07649314403533936}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15061146","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15061146","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1146/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d7e1ec7d5c544cc99b6247fa0d50c299","is_oa":false,"landing_page_url":"https://doaj.org/article/d7e1ec7d5c544cc99b6247fa0d50c299","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 6, p 1146 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/6/1146/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15061146","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 15; Issue 6; Pages: 1146","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15061146","is_oa":true,"landing_page_url":"http://dx.doi.org/10.3390/sym15061146","pdf_url":"https://www.mdpi.com/2073-8994/15/6/1146/pdf","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/7","score":0.6899999976158142,"display_name":"Affordable and clean energy"}],"awards":[{"id":"https://openalex.org/G8173364358","display_name":null,"funder_award_id":"FRF-TP-20-068A1","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4378229161.pdf","grobid_xml":"https://content.openalex.org/works/W4378229161.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W587555435","https://openalex.org/W1965757759","https://openalex.org/W1989955731","https://openalex.org/W2045701663","https://openalex.org/W2049161806","https://openalex.org/W2084367325","https://openalex.org/W2092425184","https://openalex.org/W2112119367","https://openalex.org/W2155579513","https://openalex.org/W2340680806","https://openalex.org/W2341074930","https://openalex.org/W2374612378","https://openalex.org/W2460678746","https://openalex.org/W2519905446","https://openalex.org/W2534184263","https://openalex.org/W2562896987","https://openalex.org/W2781605864","https://openalex.org/W2787103759","https://openalex.org/W2943648831","https://openalex.org/W2947056241","https://openalex.org/W3097938112","https://openalex.org/W3099283869","https://openalex.org/W3099411820","https://openalex.org/W3100209397","https://openalex.org/W3103427077","https://openalex.org/W3141901031","https://openalex.org/W3197126309","https://openalex.org/W3206956769","https://openalex.org/W3209416867","https://openalex.org/W3217008003","https://openalex.org/W4205727720","https://openalex.org/W6641835042"],"related_works":["https://openalex.org/W2359381322","https://openalex.org/W2076925422","https://openalex.org/W4298314373","https://openalex.org/W17130399","https://openalex.org/W101992021","https://openalex.org/W4230855783","https://openalex.org/W1972672132","https://openalex.org/W2098447220","https://openalex.org/W2050141483","https://openalex.org/W4309930262"],"abstract_inverted_index":{"We":[0],"propose":[1],"explicit":[2,5,57,67,122,125],"K-symplectic":[3,20,58,123],"and":[4,36,90,96,103,124,135],"symplectic-like":[6,68,80,126],"methods":[7,21,59,69,81,127],"for":[8,60,73],"the":[9,42,46,61,74,86,92,100,104,115,121,144,147,151,157,163],"charged":[10,26,63,76],"particle":[11,27,64,77],"system":[12,28],"in":[13,33,52,131,150],"a":[14,34,37],"general":[15,152],"strong":[16,153],"magnetic":[17,47,154],"field.":[18],"The":[19,25,79,107],"are":[22,82],"also":[23,141],"symmetric.":[24],"can":[29,49,70],"be":[30,50,71],"expressed":[31],"both":[32],"canonical":[35,75],"non-canonical":[38,62],"Hamiltonian":[39],"system.":[40,78],"If":[41],"three":[43],"components":[44],"of":[45,146,166],"field":[48,155],"integrated":[51],"closed":[53],"forms,":[54],"we":[55],"construct":[56],"system;":[65],"otherwise,":[66],"constructed":[72,83],"by":[84,98],"extending":[85],"original":[87],"phase":[88],"space":[89],"obtaining":[91],"augmented":[93],"separable":[94],"Hamiltonian,":[95],"then":[97],"using":[99],"splitting":[101],"method":[102,159],"midpoint":[105],"permutation.":[106],"numerical":[108],"experiments":[109],"have":[110,128],"shown":[111,142],"that":[112,143],"compared":[113],"with":[114],"higher":[116,136],"order":[117],"implicit":[118],"Runge-Kutta":[119,158],"method,":[120],"obvious":[129],"advantages":[130],"long-term":[132],"energy":[133],"conservation":[134],"computational":[137],"efficiency.":[138],"It":[139],"is":[140,160],"influence":[145],"parameter":[148],"\u03b5":[149],"on":[156],"bigger":[161],"than":[162],"two":[164],"kinds":[165],"symplectic":[167],"methods.":[168]},"counts_by_year":[{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}