{"id":"https://openalex.org/W2795150153","doi":"https://doi.org/10.1137/17m1122347","title":"An Efficient Second-Order Finite Difference Method for the One-Dimensional Schr\u00f6dinger Equation with Absorbing Boundary Conditions","display_name":"An Efficient Second-Order Finite Difference Method for the One-Dimensional Schr\u00f6dinger Equation with Absorbing Boundary Conditions","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2795150153","doi":"https://doi.org/10.1137/17m1122347","mag":"2795150153"},"language":"en","primary_location":{"id":"doi:10.1137/17m1122347","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1122347","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":true,"oa_status":"green","oa_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98627/1/17m1122347.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":true,"raw_author_name":"Buyang Li","raw_affiliation_strings":["Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong","institution_ids":["https://openalex.org/I14243506"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100353048","display_name":"Jiwei Zhang","orcid":"https://orcid.org/0000-0002-4493-7431"},"institutions":[{"id":"https://openalex.org/I4210139958","display_name":"Beijing Computational Science Research Center","ror":"https://ror.org/04tavf782","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210139958"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiwei Zhang","raw_affiliation_strings":["Beijing Computational Science Research Center, Beijing 100193, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Beijing Computational Science Research Center, Beijing 100193, People's Republic of China","institution_ids":["https://openalex.org/I4210139958"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102804383","display_name":"Chunxiong Zheng","orcid":"https://orcid.org/0000-0001-5735-633X"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunxiong Zheng","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of China","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5039197834"],"corresponding_institution_ids":["https://openalex.org/I14243506"],"apc_list":null,"apc_paid":null,"fwci":0.9159,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.7581076,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"56","issue":"2","first_page":"766","last_page":"791"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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":0.9998999834060669,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9965000152587891,"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/T11416","display_name":"Numerical methods for differential equations","score":0.996399998664856,"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/mathematics","display_name":"Mathematics","score":0.88736891746521},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5871906280517578},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5025076866149902},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.45775094628334045},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.45610079169273376},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4541485011577606},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.44391894340515137},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.41553473472595215},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.39439889788627625}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.88736891746521},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5871906280517578},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5025076866149902},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.45775094628334045},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.45610079169273376},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4541485011577606},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.44391894340515137},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.41553473472595215},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.39439889788627625},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/17m1122347","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1122347","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:ira.lib.polyu.edu.hk:10397/98627","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/98627","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98627/1/17m1122347.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/78586","is_oa":false,"landing_page_url":"http://hdl.handle.net/10397/78586","pdf_url":null,"source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Journal/Magazine Article"}],"best_oa_location":{"id":"pmh:oai:ira.lib.polyu.edu.hk:10397/98627","is_oa":true,"landing_page_url":"http://hdl.handle.net/10397/98627","pdf_url":"http://ira.lib.polyu.edu.hk/bitstream/10397/98627/1/17m1122347.pdf","source":{"id":"https://openalex.org/S4306400205","display_name":"PolyU Institutional Research Archive (Hong Kong Polytechnic University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I14243506","host_organization_name":"Hong Kong Polytechnic University","host_organization_lineage":["https://openalex.org/I14243506"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Journal/Magazine Article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1339064538","display_name":null,"funder_award_id":"11771035","funder_id":"https://openalex.org/F4320336475","funder_display_name":"National Safety Academic Fund"},{"id":"https://openalex.org/G1364899216","display_name":null,"funder_award_id":"U1530401","funder_id":"https://openalex.org/F4320336475","funder_display_name":"National Safety Academic Fund"},{"id":"https://openalex.org/G2207258740","display_name":null,"funder_award_id":"U153040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2746842099","display_name":null,"funder_award_id":"91430216","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3129806459","display_name":null,"funder_award_id":"11371218","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3912101811","display_name":null,"funder_award_id":"91630205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G391238517","display_name":null,"funder_award_id":", and","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5405721928","display_name":null,"funder_award_id":"U1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6177470129","display_name":null,"funder_award_id":"1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7416528769","display_name":null,"funder_award_id":"11771248","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7885927421","display_name":null,"funder_award_id":"1177124","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8774095616","display_name":null,"funder_award_id":"NSAF U153040","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G890820059","display_name":null,"funder_award_id":"11771035","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8935706417","display_name":null,"funder_award_id":"NSAF U1530401","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320336475","display_name":"National Safety Academic Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2795150153.pdf","grobid_xml":"https://content.openalex.org/works/W2795150153.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W193865898","https://openalex.org/W1679644037","https://openalex.org/W1967526964","https://openalex.org/W1970902446","https://openalex.org/W1972324900","https://openalex.org/W1978147630","https://openalex.org/W1979313496","https://openalex.org/W1984599860","https://openalex.org/W1991152766","https://openalex.org/W1996201390","https://openalex.org/W1997407071","https://openalex.org/W2009772969","https://openalex.org/W2009837750","https://openalex.org/W2009949889","https://openalex.org/W2010790211","https://openalex.org/W2011572440","https://openalex.org/W2014496150","https://openalex.org/W2026508990","https://openalex.org/W2029621220","https://openalex.org/W2031029580","https://openalex.org/W2031771245","https://openalex.org/W2031814558","https://openalex.org/W2040797028","https://openalex.org/W2044320610","https://openalex.org/W2053321625","https://openalex.org/W2083561837","https://openalex.org/W2104875626","https://openalex.org/W2106494524","https://openalex.org/W2120284715","https://openalex.org/W2125526756","https://openalex.org/W2154050526","https://openalex.org/W2155858022","https://openalex.org/W2334590741","https://openalex.org/W3148434010","https://openalex.org/W3151629361"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W2133690079","https://openalex.org/W4251142058","https://openalex.org/W1965041963","https://openalex.org/W2111215486","https://openalex.org/W2007426143"],"abstract_inverted_index":{"A":[0],"stable":[1,75],"and":[2,58,110],"convergent":[3],"second-order":[4],"fully":[5,69],"discrete":[6,70],"finite":[7],"difference":[8],"scheme":[9,72],"with":[10],"efficient":[11],"approximation":[12,32],"of":[13,26,39,79,114],"the":[14,23,27,36,40,45,55,60,68,77,98,107,112,115],"exact":[15],"absorbing":[16],"boundary":[17],"conditions":[18],"is":[19,33,73,82,95],"proposed":[20,116],"to":[21,54,105],"solve":[22],"Cauchy":[24],"problem":[25],"one-dimensional":[28],"Schr\u00f6dinger":[29],"equation.":[30],"Our":[31],"based":[34],"on":[35],"Pad\u00e9":[37,80],"expansion":[38,81],"square":[41],"root":[42],"function":[43],"in":[44],"complex":[46],"plane.":[47],"By":[48],"introducing":[49],"a":[50],"constant":[51],"damping":[52],"term":[53],"governing":[56],"equation":[57],"modifying":[59],"standard":[61],"Crank--Nicolson":[62],"implicit":[63],"scheme,":[64],"we":[65],"show":[66],"that":[67],"numerical":[71,99,117],"unconditionally":[74],"if":[76],"order":[78],"chosen":[83],"from":[84],"our":[85],"criterion.":[86],"In":[87],"this":[88],"case,":[89],"an":[90],"optimal-order":[91],"asymptotic":[92],"error":[93],"estimate":[94],"proved":[96],"for":[97],"solutions.":[100],"Numerical":[101],"examples":[102],"are":[103],"provided":[104],"support":[106],"theoretical":[108],"analysis":[109],"illustrate":[111],"performance":[113],"scheme.":[118]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}