{"id":"https://openalex.org/W4319601642","doi":"https://doi.org/10.1007/s10915-023-02108-6","title":"Unconditional Convergence of Conservative Spectral Galerkin Methods for the Coupled Fractional Nonlinear Klein\u2013Gordon\u2013Schr\u00f6dinger Equations","display_name":"Unconditional Convergence of Conservative Spectral Galerkin Methods for the Coupled Fractional Nonlinear Klein\u2013Gordon\u2013Schr\u00f6dinger Equations","publication_year":2023,"publication_date":"2023-02-08","ids":{"openalex":"https://openalex.org/W4319601642","doi":"https://doi.org/10.1007/s10915-023-02108-6"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-023-02108-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-023-02108-6","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of 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/A5033529254","display_name":"Dongdong Hu","orcid":"https://orcid.org/0000-0001-8480-9269"},"institutions":[{"id":"https://openalex.org/I53592917","display_name":"Jiangxi Normal University","ror":"https://ror.org/05nkgk822","country_code":"CN","type":"education","lineage":["https://openalex.org/I53592917"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Dongdong Hu","raw_affiliation_strings":["Jiangxi Provincial Center for Applied Mathematics, and School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, China"],"affiliations":[{"raw_affiliation_string":"Jiangxi Provincial Center for Applied Mathematics, and School of Mathematics and Statistics, Jiangxi Normal University, Nanchang, 330022, China","institution_ids":["https://openalex.org/I53592917"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003761715","display_name":"Yayun Fu","orcid":null},"institutions":[{"id":"https://openalex.org/I903994226","display_name":"Xuchang University","ror":"https://ror.org/03k174p87","country_code":"CN","type":"education","lineage":["https://openalex.org/I903994226"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yayun Fu","raw_affiliation_strings":["School of Science, Xuchang University, Xuchang, 461000, China"],"affiliations":[{"raw_affiliation_string":"School of Science, Xuchang University, Xuchang, 461000, China","institution_ids":["https://openalex.org/I903994226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060571605","display_name":"Wenjun Cai","orcid":"https://orcid.org/0000-0002-6149-3780"},"institutions":[{"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":false,"raw_author_name":"Wenjun Cai","raw_affiliation_strings":["School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China","institution_ids":["https://openalex.org/I152031979"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038670362","display_name":"Yushun Wang","orcid":"https://orcid.org/0000-0002-6200-220X"},"institutions":[{"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":false,"raw_author_name":"Yushun Wang","raw_affiliation_strings":["School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China","institution_ids":["https://openalex.org/I152031979"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5033529254"],"corresponding_institution_ids":["https://openalex.org/I53592917"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":2.4056,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.87804878,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"94","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","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/T11416","display_name":"Numerical methods for differential equations","score":0.9997000098228455,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8657592535018921},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5562569499015808},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5226502418518066},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5205134749412537},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5151790380477905},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5037466883659363},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4581843912601471},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.44362419843673706},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4411603808403015},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4230133891105652},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4157179594039917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3676171898841858},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.3593694567680359},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.21747854351997375},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.08887016773223877}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8657592535018921},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5562569499015808},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5226502418518066},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5205134749412537},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5151790380477905},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5037466883659363},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4581843912601471},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.44362419843673706},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4411603808403015},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4230133891105652},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4157179594039917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3676171898841858},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3593694567680359},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.21747854351997375},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.08887016773223877},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"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:10.1007/s10915-023-02108-6","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-023-02108-6","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8199999928474426}],"awards":[{"id":"https://openalex.org/G2593708604","display_name":null,"funder_award_id":"11971242","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5815619107","display_name":null,"funder_award_id":"12171245","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":42,"referenced_works":["https://openalex.org/W587555435","https://openalex.org/W1544770838","https://openalex.org/W1974658023","https://openalex.org/W1974670548","https://openalex.org/W1991925980","https://openalex.org/W1994595286","https://openalex.org/W2003202721","https://openalex.org/W2003706036","https://openalex.org/W2011095781","https://openalex.org/W2014666630","https://openalex.org/W2023545452","https://openalex.org/W2079688335","https://openalex.org/W2086574007","https://openalex.org/W2115289219","https://openalex.org/W2138580770","https://openalex.org/W2271295549","https://openalex.org/W2327218125","https://openalex.org/W2340680806","https://openalex.org/W2552236073","https://openalex.org/W2735733562","https://openalex.org/W2766149883","https://openalex.org/W2907172426","https://openalex.org/W2928920989","https://openalex.org/W2930191494","https://openalex.org/W2951529869","https://openalex.org/W2954099305","https://openalex.org/W2963006800","https://openalex.org/W2969496403","https://openalex.org/W2969630417","https://openalex.org/W2969757884","https://openalex.org/W2998314492","https://openalex.org/W3017667019","https://openalex.org/W3024213355","https://openalex.org/W3039050901","https://openalex.org/W3040082282","https://openalex.org/W3103467110","https://openalex.org/W3106538158","https://openalex.org/W3124467757","https://openalex.org/W3205863231","https://openalex.org/W3211679205","https://openalex.org/W4241341410","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W2162026849","https://openalex.org/W2394687667","https://openalex.org/W2020570337","https://openalex.org/W1970590191","https://openalex.org/W3089734727","https://openalex.org/W2056658486","https://openalex.org/W2978094276","https://openalex.org/W2903909398","https://openalex.org/W1983650744","https://openalex.org/W2096756136"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
