{"id":"https://openalex.org/W4360585977","doi":"https://doi.org/10.3934/nhm.2023042","title":"Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations","display_name":"Convergence of an energy-preserving finite difference method for the nonlinear coupled space-fractional Klein-Gordon equations","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4360585977","doi":"https://doi.org/10.3934/nhm.2023042"},"language":"en","primary_location":{"id":"doi:10.3934/nhm.2023042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023042","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://doi.org/10.3934/nhm.2023042","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100400716","display_name":"Min Li","orcid":"https://orcid.org/0000-0002-0047-2804"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Li","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101803422","display_name":"Ming Ju","orcid":"https://orcid.org/0000-0002-3698-5687"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ju Ming","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074665094","display_name":"Tingting Qin","orcid":"https://orcid.org/0000-0001-7850-707X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingting Qin","raw_affiliation_strings":["School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018602419","display_name":"Boya Zhou","orcid":"https://orcid.org/0000-0001-6082-048X"},"institutions":[{"id":"https://openalex.org/I47720641","display_name":"Huazhong University of Science and Technology","ror":"https://ror.org/00p991c53","country_code":"CN","type":"education","lineage":["https://openalex.org/I47720641"]},{"id":"https://openalex.org/I14894300","display_name":"Foshan University","ror":"https://ror.org/02xvvvp28","country_code":"CN","type":"education","lineage":["https://openalex.org/I14894300"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Boya Zhou","raw_affiliation_strings":["School of Mathematics and Big Data, Foshan University, Guangdong, 52800, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China","School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Big Data, Foshan University, Guangdong, 52800, China","institution_ids":["https://openalex.org/I14894300"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China, and Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China","institution_ids":["https://openalex.org/I47720641"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, Hubei, China","institution_ids":["https://openalex.org/I47720641"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018602419"],"corresponding_institution_ids":["https://openalex.org/I14894300","https://openalex.org/I47720641"],"apc_list":null,"apc_paid":null,"fwci":0.4486,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55100651,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"18","issue":"3","first_page":"957","last_page":"981"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9983999729156494,"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":0.7703473567962646},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6549373865127563},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.6409313082695007},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6257012486457825},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.5520053505897522},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5258044600486755},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5005490779876709},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44685015082359314},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.44677144289016724},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4387417435646057},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.4337783753871918},{"id":"https://openalex.org/keywords/energy","display_name":"Energy (signal processing)","score":0.43306058645248413},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4222186803817749},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1789214313030243},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07687082886695862}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7703473567962646},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6549373865127563},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.6409313082695007},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6257012486457825},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.5520053505897522},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5258044600486755},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5005490779876709},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44685015082359314},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.44677144289016724},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4387417435646057},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.4337783753871918},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.43306058645248413},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4222186803817749},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1789214313030243},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07687082886695862},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3934/nhm.2023042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023042","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:44ad6c931a26411b95126d3b57e33779","is_oa":true,"landing_page_url":"https://doaj.org/article/44ad6c931a26411b95126d3b57e33779","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Networks and Heterogeneous Media, Vol 18, Iss 3, Pp 957-981 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3934/nhm.2023042","is_oa":true,"landing_page_url":"https://doi.org/10.3934/nhm.2023042","pdf_url":null,"source":{"id":"https://openalex.org/S21752972","display_name":"Networks and Heterogeneous Media","issn_l":"1556-1801","issn":["1556-1801","1556-181X"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315844","host_organization_name":"American Institute of Mathematical Sciences","host_organization_lineage":["https://openalex.org/P4310315844"],"host_organization_lineage_names":["American Institute of Mathematical Sciences"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Networks and Heterogeneous Media","raw_type":"journal-article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.46000000834465027,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1644929731","https://openalex.org/W1984432912","https://openalex.org/W1990480308","https://openalex.org/W2001255400","https://openalex.org/W2001544532","https://openalex.org/W2007638845","https://openalex.org/W2014795350","https://openalex.org/W2029005334","https://openalex.org/W2038670586","https://openalex.org/W2048345092","https://openalex.org/W2056316273","https://openalex.org/W2056390784","https://openalex.org/W2068610405","https://openalex.org/W2072536983","https://openalex.org/W2096004660","https://openalex.org/W2238668211","https://openalex.org/W2560013338","https://openalex.org/W2782480706","https://openalex.org/W2899982045","https://openalex.org/W2911659081","https://openalex.org/W2969232873","https://openalex.org/W2995756203","https://openalex.org/W2999454470","https://openalex.org/W3008175267","https://openalex.org/W3034535769","https://openalex.org/W3038861442","https://openalex.org/W3045850607","https://openalex.org/W3048767891","https://openalex.org/W3159451643","https://openalex.org/W3188418281","https://openalex.org/W3190370029","https://openalex.org/W3200434296","https://openalex.org/W3215989960","https://openalex.org/W4200102304","https://openalex.org/W4230538317","https://openalex.org/W4283767083","https://openalex.org/W4294267599","https://openalex.org/W4320473675"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W4223576334","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2384221708"],"abstract_inverted_index":{"&lt;abstract&gt;&lt;p&gt;An":[0],"energy-preserving":[1],"finite":[2],"difference":[3],"method":[4],"is":[5],"first":[6],"presented":[7],"for":[8],"solving":[9],"the":[10,23,29,39,45,59],"nonlinear":[11],"coupled":[12],"space-fractional":[13],"Klein-Gordon":[14],"(KG)":[15],"equations.":[16],"The":[17],"discrete":[18],"conservation":[19],"law,":[20],"boundedness":[21],"of":[22,28],"numerical":[24,30],"solutions":[25],"and":[26,49],"convergence":[27],"schemes":[31],"are":[32,36,54],"obtained.":[33],"These":[34],"results":[35],"proved":[37],"by":[38],"recent":[40],"developed":[41],"fractional":[42],"Sobolev":[43],"inequalities,":[44],"matrix":[46],"analytical":[47],"methods":[48],"so":[50],"on.":[51],"Numerical":[52],"experiments":[53],"carried":[55],"out":[56],"to":[57],"confirm":[58],"theoretical":[60],"findings.&lt;/p&gt;&lt;/abstract&gt;":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
