{"id":"https://openalex.org/W4281488909","doi":"https://doi.org/10.1515/cmam-2022-0057","title":"Optimal Convergence of the Newton Iterative Crank\u2013Nicolson Finite Element Method for the Nonlinear Schr\u00f6dinger Equation","display_name":"Optimal Convergence of the Newton Iterative Crank\u2013Nicolson Finite Element Method for the Nonlinear Schr\u00f6dinger Equation","publication_year":2022,"publication_date":"2022-05-24","ids":{"openalex":"https://openalex.org/W4281488909","doi":"https://doi.org/10.1515/cmam-2022-0057"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0057","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0057","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in 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/A5013442339","display_name":"Hanzhang Hu","orcid":"https://orcid.org/0000-0003-2027-6357"},"institutions":[{"id":"https://openalex.org/I160391749","display_name":"Jiaying University","ror":"https://ror.org/018jdfk45","country_code":"CN","type":"education","lineage":["https://openalex.org/I160391749"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hanzhang Hu","raw_affiliation_strings":["School of Mathematics , Jiaying University , Meizhou 514015, Guangdong , P. R. China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics , Jiaying University , Meizhou 514015, Guangdong , P. R. China","institution_ids":["https://openalex.org/I160391749"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039197834","display_name":"Buyang Li","orcid":"https://orcid.org/0000-0001-7566-3464"},"institutions":[{"id":"https://openalex.org/I14243506","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98","country_code":"HK","type":"education","lineage":["https://openalex.org/I14243506"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Buyang Li","raw_affiliation_strings":["Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong , P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics , The Hong Kong Polytechnic University , Hung Hom, Kowloon , Hong Kong , P. R. China","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5011712654","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0003-2443-3516"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics , The Chinese University of Hong Kong , Shatin, N.T. , Hong Kong , P. R. China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics , The Chinese University of Hong Kong , Shatin, N.T. , Hong Kong , P. R. China","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5011712654"],"corresponding_institution_ids":["https://openalex.org/I177725633"],"apc_list":null,"apc_paid":null,"fwci":2.473,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.87321792,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","issue":"3","first_page":"591","last_page":"612"},"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":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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":0.7787120938301086},{"id":"https://openalex.org/keywords/crank\u2013nicolson-method","display_name":"Crank\u2013Nicolson method","score":0.7528178691864014},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7113024592399597},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6667975187301636},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5911821722984314},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5491251945495605},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5473263263702393},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5204687118530273},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4977164566516876},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.49151214957237244},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47546905279159546},{"id":"https://openalex.org/keywords/local-convergence","display_name":"Local convergence","score":0.4734480082988739},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17066344618797302},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09961962699890137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7787120938301086},{"id":"https://openalex.org/C180931078","wikidata":"https://www.wikidata.org/wiki/Q588725","display_name":"Crank\u2013Nicolson method","level":3,"score":0.7528178691864014},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7113024592399597},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6667975187301636},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5911821722984314},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5491251945495605},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5473263263702393},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5204687118530273},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4977164566516876},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.49151214957237244},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47546905279159546},{"id":"https://openalex.org/C117898588","wikidata":"https://www.wikidata.org/wiki/Q6664310","display_name":"Local convergence","level":3,"score":0.4734480082988739},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17066344618797302},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09961962699890137},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2022-0057","is_oa":false,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0057","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G472187114","display_name":null,"funder_award_id":"14306719","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G4812588897","display_name":null,"funder_award_id":"15301818","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G5573378842","display_name":null,"funder_award_id":"2018A0303100016","funder_id":"https://openalex.org/F4320321921","funder_display_name":"Natural Science Foundation of Guangdong Province"},{"id":"https://openalex.org/G7573447359","display_name":null,"funder_award_id":"P0031035","funder_id":"https://openalex.org/F4320322598","funder_display_name":"Hong Kong Polytechnic University"},{"id":"https://openalex.org/G8568793287","display_name":null,"funder_award_id":"14306921","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"}],"funders":[{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320321921","display_name":"Natural Science Foundation of Guangdong Province","ror":null},{"id":"https://openalex.org/F4320322598","display_name":"Hong Kong Polytechnic University","ror":"https://ror.org/0030zas98"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1973279410","https://openalex.org/W2006043132","https://openalex.org/W2015829426","https://openalex.org/W2029830616","https://openalex.org/W2031186887","https://openalex.org/W2058992888","https://openalex.org/W2060005168","https://openalex.org/W2061904552","https://openalex.org/W2064479203","https://openalex.org/W2066944044","https://openalex.org/W2075696551","https://openalex.org/W2078210968","https://openalex.org/W2486911800","https://openalex.org/W2533460754","https://openalex.org/W2963552123","https://openalex.org/W2964580220","https://openalex.org/W2969496403","https://openalex.org/W3103467110","https://openalex.org/W3171417514","https://openalex.org/W3187902182","https://openalex.org/W3204708751","https://openalex.org/W4293106097"],"related_works":["https://openalex.org/W2350788688","https://openalex.org/W2358591430","https://openalex.org/W2103912232","https://openalex.org/W2031390949","https://openalex.org/W2026900827","https://openalex.org/W3094698614","https://openalex.org/W1964267519","https://openalex.org/W3180920337","https://openalex.org/W3140142921","https://openalex.org/W4308670056"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"error":[2],"estimate":[3],"is":[4,38],"presented":[5],"for":[6,14,64],"the":[7,15,26,41,51,56,59],"Newton":[8,42],"iterative":[9,43],"Crank\u2013Nicolson":[10,61],"finite":[11],"element":[12],"method":[13,62],"nonlinear":[16],"Schr\u00f6dinger":[17],"equation,":[18],"fully":[19],"discretized":[20],"by":[21],"quadrature,":[22],"without":[23],"restriction":[24],"on":[25],"grid":[27],"ratio":[28],"between":[29],"temporal":[30],"step":[31],"size":[32],"and":[33,74],"spatial":[34],"mesh":[35],"size.":[36],"It":[37],"shown":[39],"that":[40],"solution":[44,57],"converges":[45],"double":[46],"exponentially":[47],"with":[48,68],"respect":[49],"to":[50,55],"number":[52],"of":[53,58],"iterations":[54],"implicit":[60],"uniformly":[63],"all":[65],"time":[66],"levels,":[67],"optimal":[69],"convergence":[70],"in":[71],"both":[72],"space":[73],"time.":[75]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
