{"id":"https://openalex.org/W2976853087","doi":"https://doi.org/10.1142/s1793962323500447","title":"Strang splitting schemes for<i>N</i>-level Bloch models","display_name":"Strang splitting schemes for<i>N</i>-level Bloch models","publication_year":2023,"publication_date":"2023-04-14","ids":{"openalex":"https://openalex.org/W2976853087","doi":"https://doi.org/10.1142/s1793962323500447","mag":"2976853087"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962323500447","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962323500447","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1909.10932","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074201816","display_name":"Marc E. Songolo","orcid":null},"institutions":[{"id":"https://openalex.org/I134231150","display_name":"University of Lubumbashi","ror":"https://ror.org/01mn7k054","country_code":"CD","type":"education","lineage":["https://openalex.org/I134231150"]}],"countries":["CD"],"is_corresponding":true,"raw_author_name":"Marc E. Songolo","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Lubumbashi, 1825 Lubumbashi, Republic Democratic of Congo"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Lubumbashi, 1825 Lubumbashi, Republic Democratic of Congo","institution_ids":["https://openalex.org/I134231150"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074669961","display_name":"Brigitte Bid\u00e9garay-Fesquet","orcid":"https://orcid.org/0000-0003-4221-5109"},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"funder","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210149092","display_name":"Laboratoire Jean Kuntzmann","ror":"https://ror.org/04ett5b41","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I4210149092","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I106785703","display_name":"Institut polytechnique de Grenoble","ror":"https://ror.org/05sbt2524","country_code":"FR","type":"education","lineage":["https://openalex.org/I106785703","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I899635006","display_name":"Universit\u00e9 Grenoble Alpes","ror":"https://ror.org/02rx3b187","country_code":"FR","type":"education","lineage":["https://openalex.org/I899635006"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Brigitte Bid\u00e9garay-Fesquet","raw_affiliation_strings":["Univ. Grenoble Alpes, CNRS, Grenoble INP\u2020, LJK, 38000 Grenoble, France"],"affiliations":[{"raw_affiliation_string":"Univ. Grenoble Alpes, CNRS, Grenoble INP\u2020, LJK, 38000 Grenoble, France","institution_ids":["https://openalex.org/I4210149092","https://openalex.org/I1294671590","https://openalex.org/I899635006","https://openalex.org/I106785703"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074201816"],"corresponding_institution_ids":["https://openalex.org/I134231150"],"apc_list":null,"apc_paid":null,"fwci":0.612,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.66229256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"03","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11187","display_name":"Nonlinear Dynamics and Pattern Formation","score":0.9983000159263611,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9977999925613403,"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/scheme","display_name":"Scheme (mathematics)","score":0.6931310892105103},{"id":"https://openalex.org/keywords/bloch-equations","display_name":"Bloch equations","score":0.6797478199005127},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5804198384284973},{"id":"https://openalex.org/keywords/bloch-wave","display_name":"Bloch wave","score":0.524596631526947},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5242729187011719},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5196655988693237},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.5156408548355103},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.49674540758132935},{"id":"https://openalex.org/keywords/exact-solutions-in-general-relativity","display_name":"Exact solutions in general relativity","score":0.4205586910247803},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3244677782058716},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20833662152290344},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10763031244277954},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.08705410361289978}],"concepts":[{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6931310892105103},{"id":"https://openalex.org/C142951617","wikidata":"https://www.wikidata.org/wiki/Q651707","display_name":"Bloch equations","level":2,"score":0.6797478199005127},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5804198384284973},{"id":"https://openalex.org/C37689646","wikidata":"https://www.wikidata.org/wiki/Q4454926","display_name":"Bloch wave","level":2,"score":0.524596631526947},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5242729187011719},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5196655988693237},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.5156408548355103},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.49674540758132935},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.4205586910247803},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3244677782058716},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20833662152290344},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10763031244277954},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.08705410361289978},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1142/s1793962323500447","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962323500447","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1909.10932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10932","pdf_url":"https://arxiv.org/pdf/1909.10932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},{"id":"pmh:oai:HAL:hal-02294954v1","is_oa":true,"landing_page_url":"https://hal.science/hal-02294954","pdf_url":"https://hal.science/hal-02294954/document","source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing, 2023, 14 (3), pp.2350044. &#x27E8;10.1142/S1793962323500447&#x27E9;","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1909.10932","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1909.10932","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1909.10932","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1909.10932","pdf_url":"https://arxiv.org/pdf/1909.10932","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W258533868","https://openalex.org/W367327691","https://openalex.org/W603207913","https://openalex.org/W1499509877","https://openalex.org/W1585641754","https://openalex.org/W1967872632","https://openalex.org/W1986133905","https://openalex.org/W1992447633","https://openalex.org/W2029844829","https://openalex.org/W2042157121","https://openalex.org/W2047366273","https://openalex.org/W2049161806","https://openalex.org/W2051619051","https://openalex.org/W2062951693","https://openalex.org/W2088447725","https://openalex.org/W2091453336","https://openalex.org/W2106565812","https://openalex.org/W2148372998","https://openalex.org/W2148734504","https://openalex.org/W2149864253","https://openalex.org/W2167452050","https://openalex.org/W2463396137","https://openalex.org/W2485029991","https://openalex.org/W2490140790","https://openalex.org/W2592050209","https://openalex.org/W2793703231","https://openalex.org/W3004350485","https://openalex.org/W3101180467","https://openalex.org/W4229845437","https://openalex.org/W4252872048","https://openalex.org/W4291201529","https://openalex.org/W4292914285","https://openalex.org/W4300067266","https://openalex.org/W4388394692"],"related_works":["https://openalex.org/W1970979661","https://openalex.org/W2000419049","https://openalex.org/W4317660424","https://openalex.org/W4382762952","https://openalex.org/W2046101709","https://openalex.org/W2105755740","https://openalex.org/W2067382432","https://openalex.org/W1994786786","https://openalex.org/W2119998842","https://openalex.org/W2311505222"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"we":[3,29],"define":[4],"a":[5],"splitting":[6],"scheme":[7,40],"for":[8],"the":[9,48,67,71],"N-level":[10],"Bloch":[11,49,72],"model":[12],"which":[13,28],"makes":[14],"use":[15],"of":[16,20,47,70],"exact":[17,23],"numerical":[18],"solutions":[19,24],"sub-equations.":[21],"These":[22],"involve":[25],"matrix":[26],"exponentials":[27],"want":[30],"to":[31,33,58],"avoid":[32],"calculate":[34],"at":[35],"each":[36],"time-step.":[37],"The":[38],"resulting":[39],"is":[41],"nonstandard":[42],"and":[43,53,61],"preserves":[44],"qualitative":[45],"properties":[46],"equations.":[50,73],"We":[51],"explore":[52],"compare":[54],"numerically":[55],"multiple":[56],"ways":[57],"implement":[59],"it":[60],"in":[62],"particular":[63],"take":[64],"into":[65],"account":[66],"specific":[68],"structure":[69]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2026-03-11T14:59:36.786465","created_date":"2019-10-03T00:00:00"}