{"id":"https://openalex.org/W4285042889","doi":"https://doi.org/10.1007/s11075-022-01345-4","title":"A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials","display_name":"A uniformly accurate exponential wave integrator Fourier pseudo-spectral method with structure-preservation for long-time dynamics of the Dirac equation with small potentials","publication_year":2022,"publication_date":"2022-07-11","ids":{"openalex":"https://openalex.org/W4285042889","doi":"https://doi.org/10.1007/s11075-022-01345-4"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-022-01345-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01345-4","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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, People\u2019s Republic of China","Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang, People\u2019s Republic of China","Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, People\u2019s Republic of China","College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China"],"raw_orcid":"https://orcid.org/0000-0002-9573-989X","affiliations":[{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, 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, People\u2019s Republic of China","institution_ids":[]},{"raw_affiliation_string":"Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang, People\u2019s Republic of China","institution_ids":[]},{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China","institution_ids":["https://openalex.org/I94611258"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100539485","display_name":"Liqing Zhu","orcid":null},"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":"Liqing Zhu","raw_affiliation_strings":["College of Mathematics Science, Hebei Normal University, Shijiazhuang, People\u2019s Republic of China","College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, People\u2019s Republic of China","institution_ids":["https://openalex.org/I94611258"]},{"raw_affiliation_string":"College of Mathematics Science, Hebei Normal University, Shijiazhuang, 050024, People\u2019s Republic of China","institution_ids":["https://openalex.org/I94611258"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5087013025","https://openalex.org/A5100539485"],"corresponding_institution_ids":["https://openalex.org/I94611258"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.6365,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.88940982,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"92","issue":"2","first_page":"1367","last_page":"1401"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10248","display_name":"Nonlinear Waves and Solitons","score":0.9980999827384949,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6918807029724121},{"id":"https://openalex.org/keywords/dirac-equation","display_name":"Dirac equation","score":0.6592050790786743},{"id":"https://openalex.org/keywords/dirac","display_name":"Dirac (video compression format)","score":0.57486492395401},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5356838703155518},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.5325030088424683},{"id":"https://openalex.org/keywords/dirac-comb","display_name":"Dirac comb","score":0.4979817867279053},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.46917206048965454},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.4685322642326355},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4424200654029846},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.2792447805404663},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.23417308926582336},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23385873436927795},{"id":"https://openalex.org/keywords/dirac-algebra","display_name":"Dirac algebra","score":0.10866764187812805}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6918807029724121},{"id":"https://openalex.org/C82601208","wikidata":"https://www.wikidata.org/wiki/Q272621","display_name":"Dirac equation","level":2,"score":0.6592050790786743},{"id":"https://openalex.org/C61039578","wikidata":"https://www.wikidata.org/wiki/Q604279","display_name":"Dirac (video compression format)","level":3,"score":0.57486492395401},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5356838703155518},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.5325030088424683},{"id":"https://openalex.org/C50953366","wikidata":"https://www.wikidata.org/wiki/Q385599","display_name":"Dirac comb","level":5,"score":0.4979817867279053},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.46917206048965454},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.4685322642326355},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4424200654029846},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.2792447805404663},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.23417308926582336},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23385873436927795},{"id":"https://openalex.org/C149545384","wikidata":"https://www.wikidata.org/wiki/Q5280160","display_name":"Dirac algebra","level":3,"score":0.10866764187812805},{"id":"https://openalex.org/C186453547","wikidata":"https://www.wikidata.org/wiki/Q2126","display_name":"Neutrino","level":2,"score":0.0},{"id":"https://openalex.org/C156785651","wikidata":"https://www.wikidata.org/wiki/Q688945","display_name":"Dirac spinor","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-022-01345-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-022-01345-4","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities","score":0.4099999964237213}],"awards":[{"id":"https://openalex.org/G6793988542","display_name":null,"funder_award_id":"A2021205036","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":54,"referenced_works":["https://openalex.org/W106404678","https://openalex.org/W1506094548","https://openalex.org/W1963558395","https://openalex.org/W1967057381","https://openalex.org/W1977644650","https://openalex.org/W1978147557","https://openalex.org/W1982686824","https://openalex.org/W1984005161","https://openalex.org/W2010040530","https://openalex.org/W2011531675","https://openalex.org/W2012344773","https://openalex.org/W2042101357","https://openalex.org/W2045505006","https://openalex.org/W2046525394","https://openalex.org/W2047270251","https://openalex.org/W2056470162","https://openalex.org/W2058122340","https://openalex.org/W2086585878","https://openalex.org/W2090561979","https://openalex.org/W2091039826","https://openalex.org/W2094781410","https://openalex.org/W2101962226","https://openalex.org/W2105685140","https://openalex.org/W2110498046","https://openalex.org/W2126279743","https://openalex.org/W2163758457","https://openalex.org/W2283547420","https://openalex.org/W2318376939","https://openalex.org/W2333238640","https://openalex.org/W2346165189","https://openalex.org/W2347163358","https://openalex.org/W2909121866","https://openalex.org/W2945834089","https://openalex.org/W2962908824","https://openalex.org/W2964168952","https://openalex.org/W2964199329","https://openalex.org/W2979799995","https://openalex.org/W3008781546","https://openalex.org/W3098636032","https://openalex.org/W3100405256","https://openalex.org/W3101304946","https://openalex.org/W3102994102","https://openalex.org/W3104073857","https://openalex.org/W3112156664","https://openalex.org/W3123381822","https://openalex.org/W3165653114","https://openalex.org/W3171923093","https://openalex.org/W3181875108","https://openalex.org/W3202832609","https://openalex.org/W3204714066","https://openalex.org/W3212816381","https://openalex.org/W4211077197","https://openalex.org/W4220675544","https://openalex.org/W4253937035"],"related_works":["https://openalex.org/W1564485841","https://openalex.org/W4287219806","https://openalex.org/W4244688541","https://openalex.org/W105939817","https://openalex.org/W3100754759","https://openalex.org/W2951283098","https://openalex.org/W105150783","https://openalex.org/W2326064537","https://openalex.org/W1612231772","https://openalex.org/W1919901593"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}
