{"id":"https://openalex.org/W2083191882","doi":"https://doi.org/10.1137/050629823","title":"Strang Splitting for the Time-Dependent Schr\u00f6dinger Equation on Sparse Grids","display_name":"Strang Splitting for the Time-Dependent Schr\u00f6dinger Equation on Sparse Grids","publication_year":2007,"publication_date":"2007-12-20","ids":{"openalex":"https://openalex.org/W2083191882","doi":"https://doi.org/10.1137/050629823","mag":"2083191882"},"language":"en","primary_location":{"id":"doi:10.1137/050629823","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629823","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","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/A5050779118","display_name":"Vasile Gradinaru","orcid":"https://orcid.org/0000-0002-7762-7894"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"V. Gradinaru","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5050779118"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5899,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.92653258,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"46","issue":"1","first_page":"103","last_page":"123"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9995999932289124,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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/discretization","display_name":"Discretization","score":0.8213162422180176},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.778967022895813},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6630758047103882},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6208499670028687},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5451934933662415},{"id":"https://openalex.org/keywords/schr\u00f6dinger-equation","display_name":"Schr\u00f6dinger equation","score":0.5305051803588867},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.48505300283432007},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4561057686805725},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43229907751083374},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4289347529411316},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.4134748578071594},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1868019998073578},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09965783357620239},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08737185597419739}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8213162422180176},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.778967022895813},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6630758047103882},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6208499670028687},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5451934933662415},{"id":"https://openalex.org/C63036615","wikidata":"https://www.wikidata.org/wiki/Q165498","display_name":"Schr\u00f6dinger equation","level":2,"score":0.5305051803588867},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.48505300283432007},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4561057686805725},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43229907751083374},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4289347529411316},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.4134748578071594},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1868019998073578},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09965783357620239},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08737185597419739},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050629823","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050629823","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.69.3379","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.69.3379","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://na.uni-tuebingen.de/~gradinar/SplTDSEtheo.pdf","raw_type":"text"},{"id":"pmh:oai:bibcyt.ucla.edu.ve:T070300015738/5","is_oa":false,"landing_page_url":"http://bibcyt.ucla.edu.ve/cgi-win/be_alex.exe?Acceso=T070300015738/5&Nombrebd=Bciucla","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6899999976158142,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W188371495","https://openalex.org/W198142710","https://openalex.org/W246015835","https://openalex.org/W573267195","https://openalex.org/W1459519259","https://openalex.org/W1490180844","https://openalex.org/W1494602634","https://openalex.org/W1539318315","https://openalex.org/W1558122728","https://openalex.org/W1592378316","https://openalex.org/W1805381866","https://openalex.org/W1967026886","https://openalex.org/W1975238525","https://openalex.org/W1995285013","https://openalex.org/W2012708209","https://openalex.org/W2017276053","https://openalex.org/W2035087858","https://openalex.org/W2036017515","https://openalex.org/W2039277199","https://openalex.org/W2041530119","https://openalex.org/W2044087434","https://openalex.org/W2068987297","https://openalex.org/W2070656880","https://openalex.org/W2083255279","https://openalex.org/W2092200004","https://openalex.org/W2116514123","https://openalex.org/W2131778920","https://openalex.org/W2132119675","https://openalex.org/W2164751878","https://openalex.org/W2321775062","https://openalex.org/W2403013574","https://openalex.org/W2749942571","https://openalex.org/W2798679239","https://openalex.org/W2983621325","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W1493245244","https://openalex.org/W3012733398"],"abstract_inverted_index":{"The":[0,14],"time-dependent":[1],"Schr\u00f6dinger":[2],"equation":[3],"is":[4,53,66],"discretized":[5],"in":[6,28,68],"space":[7,70],"by":[8],"a":[9],"sparse":[10],"grid":[11,47],"pseudospectral":[12],"method.":[13],"Strang":[15],"splitting":[16],"for":[17,63],"the":[18,32,35,39,45,50,54,57,60,64,69],"resulting":[19],"evolutionary":[20],"problem":[21],"features":[22],"first":[23],"or":[24],"second":[25],"order":[26],"convergence":[27,65],"time,":[29],"depending":[30],"on":[31],"smoothness":[33],"of":[34,38,59],"potential":[36],"and":[37],"initial":[40],"data.":[41],"In":[42],"contrast":[43],"to":[44],"full":[46],"case,":[48],"where":[49],"frequency":[51],"domain":[52],"working":[55],"place,":[56],"proof":[58],"sufficient":[61],"conditions":[62],"done":[67],"realm.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
