{"id":"https://openalex.org/W4289333586","doi":"https://doi.org/10.1137/21m1452020","title":"Linearly Implicit Invariant-Preserving Decoupled Difference Scheme For The Rotation-Two-Component Camassa--Holm System","display_name":"Linearly Implicit Invariant-Preserving Decoupled Difference Scheme For The Rotation-Two-Component Camassa--Holm System","publication_year":2022,"publication_date":"2022-08-01","ids":{"openalex":"https://openalex.org/W4289333586","doi":"https://doi.org/10.1137/21m1452020"},"language":"en","primary_location":{"id":"doi:10.1137/21m1452020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1452020","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5100661021","display_name":"Qifeng Zhang","orcid":"https://orcid.org/0000-0002-2742-2188"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qifeng Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100614787","display_name":"Lingling Liu","orcid":"https://orcid.org/0000-0001-8165-0475"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lingling Liu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100406530","display_name":"Zhimin Zhang","orcid":"https://orcid.org/0000-0002-9394-9586"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhimin Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2203,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78389355,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":98},"biblio":{"volume":"44","issue":"4","first_page":"A2226","last_page":"A2252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9912999868392944,"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"}},{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9846000075340271,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8749868273735046},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.6293569207191467},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6185725331306458},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.49703195691108704},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.49458667635917664},{"id":"https://openalex.org/keywords/conservation-of-mass","display_name":"Conservation of mass","score":0.45001477003097534},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.437974214553833},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.13212385773658752}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8749868273735046},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.6293569207191467},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6185725331306458},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.49703195691108704},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49458667635917664},{"id":"https://openalex.org/C157206272","wikidata":"https://www.wikidata.org/wiki/Q483948","display_name":"Conservation of mass","level":2,"score":0.45001477003097534},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.437974214553833},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.13212385773658752},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1452020","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1452020","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4646362747","display_name":"\u7535\u78c1\u573a\u65b9\u7a0b\u53ca\u5176\u7279\u5f81\u503c\u95ee\u9898\u9ad8\u6548\u9ad8\u7cbe\u5ea6\u6570\u503c\u65b9\u6cd5","funder_award_id":"11871092","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4797210442","display_name":null,"funder_award_id":"U1930402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7794165260","display_name":null,"funder_award_id":"12131005","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"},{"id":"https://openalex.org/F4320324847","display_name":"Zhejiang Sci-Tech University","ror":"https://ror.org/03893we55"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":50,"referenced_works":["https://openalex.org/W1527832896","https://openalex.org/W1964630003","https://openalex.org/W1971335301","https://openalex.org/W1971420721","https://openalex.org/W1976021283","https://openalex.org/W1986208932","https://openalex.org/W1992001246","https://openalex.org/W1992361999","https://openalex.org/W1996480499","https://openalex.org/W2011775793","https://openalex.org/W2015749938","https://openalex.org/W2021921796","https://openalex.org/W2026031976","https://openalex.org/W2031955135","https://openalex.org/W2050870016","https://openalex.org/W2064304765","https://openalex.org/W2071969012","https://openalex.org/W2086424643","https://openalex.org/W2089285725","https://openalex.org/W2095224654","https://openalex.org/W2098801586","https://openalex.org/W2116836540","https://openalex.org/W2158429484","https://openalex.org/W2168959769","https://openalex.org/W2170576189","https://openalex.org/W2234746416","https://openalex.org/W2331216171","https://openalex.org/W2342255021","https://openalex.org/W2468131123","https://openalex.org/W2515045738","https://openalex.org/W2579871422","https://openalex.org/W2586897461","https://openalex.org/W2752342010","https://openalex.org/W2760191590","https://openalex.org/W2768799490","https://openalex.org/W2782821445","https://openalex.org/W2790667771","https://openalex.org/W2791397697","https://openalex.org/W2903515358","https://openalex.org/W2944374394","https://openalex.org/W2944890454","https://openalex.org/W2963207167","https://openalex.org/W2994611265","https://openalex.org/W3003628603","https://openalex.org/W3015377707","https://openalex.org/W3121383683","https://openalex.org/W3123354790","https://openalex.org/W3155062758","https://openalex.org/W3157255813","https://openalex.org/W3159092576"],"related_works":["https://openalex.org/W2154204858","https://openalex.org/W3209622820","https://openalex.org/W2382250648","https://openalex.org/W2367363545","https://openalex.org/W2586383879","https://openalex.org/W2067895158","https://openalex.org/W4379507409","https://openalex.org/W2066331732","https://openalex.org/W2561874146","https://openalex.org/W2291295292"],"abstract_inverted_index":{"In":[0,91],"this":[1],"paper,":[2],"we":[3],"develop,":[4],"analyze":[5],"and":[6,25,39,52,59,71,121,137],"numerically":[7],"test":[8],"an":[9],"invariant-preserving":[10],"three-level":[11],"linearized":[12],"implicit":[13],"difference":[14],"scheme":[15,48,113],"for":[16,55,65,72,95,130],"a":[17,82],"rotation-two-component":[18],"Camassa--Holm":[19],"system":[20],"[L.":[21],"Fan,":[22],"H.":[23],"Gao,":[24],"Y.":[26],"Liu,":[27],"Adv.":[28],"Math.":[29],"291":[30],"(2016),":[31],"pp.":[32],"59--89],":[33],"which":[34],"contains":[35],"strongly":[36,97],"nonlinear":[37,98],"terms":[38],"high-order":[40],"derivative":[41],"terms.":[42],"We":[43],"prove":[44],"that":[45],"the":[46,57,66,69,73,77,93,96,111,139],"numerical":[47,112,124],"is":[49,100],"uniquely":[50],"solvable":[51],"second-order":[53],"convergent":[54],"both":[56],"spatial":[58],"temporal":[60],"discretizations.":[61],"Optimal":[62],"error":[63],"estimates":[64],"velocity":[67],"in":[68,76],"$L^{\\infty}$-norm":[70],"surface":[74],"elevation":[75],"$L^2$-norm":[78],"are":[79],"obtained":[80],"under":[81],"suitable":[83],"step-size":[84],"ratio":[85],"restriction":[86],"based":[87],"on":[88],"energy":[89],"analysis.":[90],"particular,":[92],"analysis":[94],"term":[99],"carried":[101],"out":[102],"by":[103],"splitting":[104],"it":[105],"into":[106],"several":[107],"recursive":[108],"expressions.":[109],"Moreover,":[110],"preserves":[114],"at":[115],"least":[116],"two":[117],"conservation":[118],"invariants:":[119],"mass":[120],"energy.":[122],"Extensive":[123],"experiments":[125],"including":[126],"long":[127],"time":[128],"simulations":[129],"zero$/$nonzero":[131],"rotation":[132],"parameters":[133],"demonstrate":[134],"solution":[135],"behavior":[136],"verify":[138],"convergence":[140],"results":[141],"as":[142,144],"well":[143],"mass/energy":[145],"conservation.":[146]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}