{"id":"https://openalex.org/W2065163831","doi":"https://doi.org/10.1007/s10915-012-9628-1","title":"High Order Stable Finite Difference Methods for the Schr\u00f6dinger Equation","display_name":"High Order Stable Finite Difference Methods for the Schr\u00f6dinger Equation","publication_year":2012,"publication_date":"2012-08-03","ids":{"openalex":"https://openalex.org/W2065163831","doi":"https://doi.org/10.1007/s10915-012-9628-1","mag":"2065163831"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-012-9628-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-012-9628-1","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-154360","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102987223","display_name":"Anna Nissen","orcid":"https://orcid.org/0000-0002-4533-9214"},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"A. Nissen","raw_affiliation_strings":["Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA","Department of Energy Resources Engineering, Stanford University, Stanford, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Energy Resources Engineering, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004879351","display_name":"Gunilla Kreiss","orcid":"https://orcid.org/0000-0001-8865-8218"},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"G. Kreiss","raw_affiliation_strings":["Department of Information Technology, Uppsala University, Uppsala, Sweden","Department of Information Technology; Uppsala University; Uppsala Sweden"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information Technology, Uppsala University, Uppsala, Sweden","institution_ids":["https://openalex.org/I123387679"]},{"raw_affiliation_string":"Department of Information Technology; Uppsala University; Uppsala Sweden","institution_ids":["https://openalex.org/I123387679"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084385325","display_name":"Margot Gerritsen","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Gerritsen","raw_affiliation_strings":["Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA","Department of Energy Resources Engineering, Stanford University, Stanford, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Energy Resources Engineering, Stanford University, Stanford, CA, USA","institution_ids":["https://openalex.org/I97018004"]},{"raw_affiliation_string":"Department of Energy Resources Engineering, Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5102987223"],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":4.8285,"has_fulltext":false,"cited_by_count":24,"citation_normalized_percentile":{"value":0.9530837,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"55","issue":"1","first_page":"173","last_page":"199"},"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":0.9994999766349792,"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":0.9991999864578247,"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":0.8986502885818481},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5842074751853943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5413586497306824},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5357396602630615},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5115745663642883},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5068572163581848},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.505852460861206},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.49490970373153687},{"id":"https://openalex.org/keywords/closure","display_name":"Closure (psychology)","score":0.4881177842617035},{"id":"https://openalex.org/keywords/approximations-of-\u03c0","display_name":"Approximations of \u03c0","score":0.47122466564178467},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4525071084499359},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4466443955898285},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.4455045759677887},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3820306658744812},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.061653345823287964}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8986502885818481},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5842074751853943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5413586497306824},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5357396602630615},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5115745663642883},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5068572163581848},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.505852460861206},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.49490970373153687},{"id":"https://openalex.org/C146834321","wikidata":"https://www.wikidata.org/wiki/Q2979672","display_name":"Closure (psychology)","level":2,"score":0.4881177842617035},{"id":"https://openalex.org/C193386753","wikidata":"https://www.wikidata.org/wiki/Q1130396","display_name":"Approximations of \u03c0","level":2,"score":0.47122466564178467},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4525071084499359},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4466443955898285},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.4455045759677887},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3820306658744812},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.061653345823287964},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C34447519","wikidata":"https://www.wikidata.org/wiki/Q179522","display_name":"Market economy","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","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},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s10915-012-9628-1","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-012-9628-1","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.220.4286","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.220.4286","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.it.uu.se/research/reports/2011-014/2011-014-nc.pdf","raw_type":"text"},{"id":"pmh:oai:DiVA.org:uu-154360","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-154360","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"info:eu-repo/semantics/report"}],"best_oa_location":{"id":"pmh:oai:DiVA.org:uu-154360","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-154360","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"info:eu-repo/semantics/report"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"},{"id":"https://openalex.org/F4320336376","display_name":"Uppsala Multidisciplinary Center for Advanced Computational Science","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W96454744","https://openalex.org/W1538356049","https://openalex.org/W1965855805","https://openalex.org/W1966155583","https://openalex.org/W1978362527","https://openalex.org/W1986174760","https://openalex.org/W2012986376","https://openalex.org/W2029017626","https://openalex.org/W2043302021","https://openalex.org/W2049991352","https://openalex.org/W2051465806","https://openalex.org/W2066272263","https://openalex.org/W2087131616","https://openalex.org/W2120920736","https://openalex.org/W2149919761","https://openalex.org/W2151752974","https://openalex.org/W2155276545","https://openalex.org/W2157768197","https://openalex.org/W2157831252","https://openalex.org/W4212946773","https://openalex.org/W4245194646","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W1544816068","https://openalex.org/W1975234065","https://openalex.org/W4251142058","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W1965041963","https://openalex.org/W2007426143","https://openalex.org/W2384221708","https://openalex.org/W2085654163"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-02T09:51:11.867554","created_date":"2025-10-10T00:00:00"}
