{"id":"https://openalex.org/W2041905900","doi":"https://doi.org/10.1137/120866373","title":"Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schr\u00f6dinger Equations","display_name":"Convergence Analysis of High-Order Time-Splitting Pseudospectral Methods for Nonlinear Schr\u00f6dinger Equations","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2041905900","doi":"https://doi.org/10.1137/120866373","mag":"2041905900"},"language":"en","primary_location":{"id":"doi:10.1137/120866373","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120866373","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/A5111586019","display_name":"Mechthild Thalhammer","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mechthild Thalhammer","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5111586019"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6618,"has_fulltext":false,"cited_by_count":107,"citation_normalized_percentile":{"value":0.98131673,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"50","issue":"6","first_page":"3231","last_page":"3258"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","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/T10425","display_name":"Cold Atom Physics and Bose-Einstein Condensates","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"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/T11575","display_name":"Nonlinear Photonic Systems","score":0.9965999722480774,"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":0.8232783079147339},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6436283588409424},{"id":"https://openalex.org/keywords/pseudo-spectral-method","display_name":"Pseudo-spectral method","score":0.6312034130096436},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5660611391067505},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5586771368980408},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48008638620376587},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.476139098405838},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46309733390808105},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.4571615755558014},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4565422832965851},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.4247328042984009},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.41366565227508545},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.10464689135551453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8232783079147339},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6436283588409424},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.6312034130096436},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5660611391067505},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5586771368980408},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48008638620376587},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.476139098405838},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46309733390808105},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.4571615755558014},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4565422832965851},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.4247328042984009},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.41366565227508545},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.10464689135551453},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/120866373","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120866373","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"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1592378316","https://openalex.org/W1979983774","https://openalex.org/W2025314501","https://openalex.org/W2026106782","https://openalex.org/W2046913111","https://openalex.org/W2051494558","https://openalex.org/W2051611580","https://openalex.org/W2052525012","https://openalex.org/W2058066520","https://openalex.org/W2060295595","https://openalex.org/W2083561837","https://openalex.org/W2092400970","https://openalex.org/W2114363690","https://openalex.org/W2120326596","https://openalex.org/W2122716160","https://openalex.org/W2155579513","https://openalex.org/W2317460055","https://openalex.org/W2346165189","https://openalex.org/W4245463005"],"related_works":["https://openalex.org/W2027355161","https://openalex.org/W3155239281","https://openalex.org/W2006041274","https://openalex.org/W138156814","https://openalex.org/W3043844242","https://openalex.org/W4312614219","https://openalex.org/W2329802658","https://openalex.org/W2057796401","https://openalex.org/W1982237479","https://openalex.org/W2025944355"],"abstract_inverted_index":{"In":[0],"this":[1],"work,":[2],"the":[3,10,46,52,60,67,74,85,88,91,100,123,130,140,163],"issue":[4],"of":[5,15,32,54,87,112,132,143],"favorable":[6],"numerical":[7],"methods":[8,64,81,156],"for":[9,147,152],"space":[11,61],"and":[12,29,39,117,145],"time":[13,75],"discretization":[14,62],"low-dimensional":[16],"nonlinear":[17,114],"Schr\u00f6dinger":[18],"equations":[19,116,161],"is":[20,24,57,95],"addressed.":[21],"The":[22,104],"objective":[23],"to":[25,158],"provide":[26],"a":[27,43,109,133],"stability":[28],"error":[30,136],"analysis":[31,106],"high-accuracy":[33],"discretizations":[34],"that":[35],"rely":[36],"on":[37,108],"spectral":[38,102],"splitting":[40,80],"methods.":[41],"As":[42],"model":[44],"problem,":[45],"time-dependent":[47,159],"Gross--Pitaevskii":[48,160],"equation":[49,94],"arising":[50],"in":[51,97,129],"description":[53],"Bose--Einstein":[55],"condensates":[56],"considered.":[58],"For":[59,73],"pseudospectral":[63,155],"collocated":[65],"at":[66],"associated":[68],"quadrature":[69],"nodes":[70],"are":[71,82,138],"analyzed.":[72],"integration":[76],"high-order":[77],"exponential":[78],"operator":[79],"studied,":[83],"where":[84],"decomposition":[86],"function":[89],"defining":[90],"partial":[92],"differential":[93],"chosen":[96],"accordance":[98],"with":[99],"underlying":[101],"method.":[103],"convergence":[105],"relies":[107],"general":[110],"framework":[111],"abstract":[113],"evolution":[115],"fractional":[118],"power":[119],"spaces":[120],"defined":[121],"by":[122],"principal":[124],"linear":[125],"part.":[126],"Essential":[127],"tools":[128],"derivation":[131],"temporal":[134],"global":[135],"estimate":[137],"further":[139],"formal":[141],"calculus":[142],"Lie-derivatives":[144],"bounds":[146],"iterated":[148],"Lie-commutators.":[149],"Numerical":[150],"examples":[151],"higher-order":[153],"time-splitting":[154],"applied":[157],"illustrate":[162],"theoretical":[164],"result.":[165]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":10},{"year":2024,"cited_by_count":7},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":16},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":9},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
