{"id":"https://openalex.org/W3156898840","doi":"https://doi.org/10.1007/s40314-021-01508-4","title":"Analysis of a conservative fourth-order compact finite difference scheme for the Klein\u2013Gordon\u2013Dirac equation","display_name":"Analysis of a conservative fourth-order compact finite difference scheme for the Klein\u2013Gordon\u2013Dirac equation","publication_year":2021,"publication_date":"2021-04-17","ids":{"openalex":"https://openalex.org/W3156898840","doi":"https://doi.org/10.1007/s40314-021-01508-4","mag":"3156898840"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-021-01508-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01508-4","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/A5087013025","display_name":"Jiyong Li","orcid":"https://orcid.org/0000-0002-9573-989X"},"institutions":[{"id":"https://openalex.org/I94611258","display_name":"Hebei Normal University","ror":"https://ror.org/004rbbw49","country_code":"CN","type":"education","lineage":["https://openalex.org/I94611258"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiyong Li","raw_affiliation_strings":["College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China","Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang, 050024, People\u2019s Republic of China","Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People\u2019s Republic of China","College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China","institution_ids":["https://openalex.org/I94611258"]},{"raw_affiliation_string":"Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang, 050024, People\u2019s Republic of China","institution_ids":[]},{"raw_affiliation_string":"Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, 050024, People\u2019s Republic of China","institution_ids":[]},{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People's Republic of China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044135785","display_name":"Ting-Chun Wang","orcid":"https://orcid.org/0000-0002-1522-2381"},"institutions":[{"id":"https://openalex.org/I200845125","display_name":"Nanjing University of Information Science and Technology","ror":"https://ror.org/02y0rxk19","country_code":"CN","type":"education","lineage":["https://openalex.org/I200845125"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tingchun Wang","raw_affiliation_strings":["School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People\u2019s Republic of China","institution_ids":["https://openalex.org/I200845125"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, People's Republic of China","institution_ids":["https://openalex.org/I200845125"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5087013025"],"corresponding_institution_ids":["https://openalex.org/I94611258"],"apc_list":null,"apc_paid":null,"fwci":3.4124,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.91856018,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"40","issue":"4","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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/mathematics","display_name":"Mathematics","score":0.733931303024292},{"id":"https://openalex.org/keywords/klein\u2013gordon-equation","display_name":"Klein\u2013Gordon equation","score":0.7310898900032043},{"id":"https://openalex.org/keywords/compact-finite-difference","display_name":"Compact finite difference","score":0.5981228351593018},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5723047256469727},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5355721712112427},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.5056543350219727},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5040130019187927},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.49631744623184204},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.47225087881088257},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4561670422554016},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4326859712600708},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42856526374816895},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4105263948440552},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4001055359840393},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3076128661632538},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.19309654831886292},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.16996267437934875},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09909692406654358}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.733931303024292},{"id":"https://openalex.org/C101682238","wikidata":"https://www.wikidata.org/wiki/Q868967","display_name":"Klein\u2013Gordon equation","level":3,"score":0.7310898900032043},{"id":"https://openalex.org/C2780829570","wikidata":"https://www.wikidata.org/wiki/Q25113057","display_name":"Compact finite difference","level":3,"score":0.5981228351593018},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5723047256469727},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5355721712112427},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.5056543350219727},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5040130019187927},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.49631744623184204},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.47225087881088257},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4561670422554016},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4326859712600708},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42856526374816895},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4105263948440552},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4001055359840393},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3076128661632538},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.19309654831886292},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.16996267437934875},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09909692406654358},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-021-01508-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-021-01508-4","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":[],"awards":[{"id":"https://openalex.org/G1877877632","display_name":null,"funder_award_id":"A2014205136","funder_id":"https://openalex.org/F4320338335","funder_display_name":"H2020 European Research Council"}],"funders":[{"id":"https://openalex.org/F4320338335","display_name":"H2020 European Research Council","ror":"https://ror.org/0472cxd90"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W166252499","https://openalex.org/W1506094548","https://openalex.org/W1522527787","https://openalex.org/W1583945035","https://openalex.org/W1591909544","https://openalex.org/W1903353743","https://openalex.org/W1964804260","https://openalex.org/W1965471588","https://openalex.org/W1967990418","https://openalex.org/W1990784906","https://openalex.org/W1995000834","https://openalex.org/W2005963734","https://openalex.org/W2015593049","https://openalex.org/W2016661108","https://openalex.org/W2031186887","https://openalex.org/W2038480870","https://openalex.org/W2038588805","https://openalex.org/W2039433885","https://openalex.org/W2040511457","https://openalex.org/W2050338742","https://openalex.org/W2057113618","https://openalex.org/W2064049924","https://openalex.org/W2064726339","https://openalex.org/W2078004866","https://openalex.org/W2078210968","https://openalex.org/W2078311253","https://openalex.org/W2087108336","https://openalex.org/W2090708088","https://openalex.org/W2092647133","https://openalex.org/W2096760851","https://openalex.org/W2101962226","https://openalex.org/W2124382907","https://openalex.org/W2132883228","https://openalex.org/W2141790616","https://openalex.org/W2143097120","https://openalex.org/W2150511304","https://openalex.org/W2155791749","https://openalex.org/W2347163358","https://openalex.org/W2889260401","https://openalex.org/W2905066384","https://openalex.org/W2909121866","https://openalex.org/W2912950356","https://openalex.org/W2914456489","https://openalex.org/W2945834089","https://openalex.org/W2963009474","https://openalex.org/W3043395867","https://openalex.org/W3101835573","https://openalex.org/W3102994102","https://openalex.org/W3104073857","https://openalex.org/W3112156664","https://openalex.org/W3123381822","https://openalex.org/W3173960225","https://openalex.org/W3209325367"],"related_works":["https://openalex.org/W2178449688","https://openalex.org/W2530283266","https://openalex.org/W2902090247","https://openalex.org/W2005051193","https://openalex.org/W2078311253","https://openalex.org/W1791084566","https://openalex.org/W3167537737","https://openalex.org/W4388717528","https://openalex.org/W2946146460","https://openalex.org/W1564485841"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
