{"id":"https://openalex.org/W1991160236","doi":"https://doi.org/10.1137/s0036142901397435","title":"Difference Approximations for the Second Order Wave Equation","display_name":"Difference Approximations for the Second Order Wave Equation","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W1991160236","doi":"https://doi.org/10.1137/s0036142901397435","mag":"1991160236"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901397435","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901397435","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/A5113972450","display_name":"Heinz\u2010Otto Kreiss","orcid":null},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Heinz-Otto Kreiss","raw_affiliation_strings":["Lawrence Livermore National Laboratory"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008289430","display_name":"N. Anders Petersson","orcid":"https://orcid.org/0000-0003-0522-7872"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"N. Anders Petersson","raw_affiliation_strings":["Royal Inst. of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Inst. of Technology","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021162218","display_name":"Jacob Ystr\u00f6m","orcid":null},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Jacob Ystr\u00f6m","raw_affiliation_strings":["Royal Inst. of Technology"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Royal Inst. of Technology","institution_ids":["https://openalex.org/I86987016"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.7768,"has_fulltext":false,"cited_by_count":109,"citation_normalized_percentile":{"value":0.93462476,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"40","issue":"5","first_page":"1940","last_page":"1967"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9997000098228455,"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"}},"topics":[{"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":0.9991999864578247,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.8611498475074768},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8053218722343445},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.6982251405715942},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5853358507156372},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5799441337585449},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.5246042013168335},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5043119192123413},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.4944288730621338},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4545012414455414},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.45287618041038513},{"id":"https://openalex.org/keywords/wave-equation","display_name":"Wave equation","score":0.4369061589241028},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.43585440516471863}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8611498475074768},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8053218722343445},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.6982251405715942},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5853358507156372},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5799441337585449},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.5246042013168335},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5043119192123413},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.4944288730621338},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4545012414455414},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.45287618041038513},{"id":"https://openalex.org/C59696629","wikidata":"https://www.wikidata.org/wiki/Q193846","display_name":"Wave equation","level":2,"score":0.4369061589241028},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.43585440516471863},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0036142901397435","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901397435","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:10.1.1.538.4716","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.538.4716","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://computation.llnl.gov/casc/serpentine/pubs/KPYWave2002.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1538356049","https://openalex.org/W1982337594","https://openalex.org/W2005733131","https://openalex.org/W2022385500","https://openalex.org/W2059257656","https://openalex.org/W2070974335","https://openalex.org/W2080480952","https://openalex.org/W2093817972","https://openalex.org/W3133685766","https://openalex.org/W4212946773","https://openalex.org/W4255234192"],"related_works":["https://openalex.org/W1966914714","https://openalex.org/W1616145305","https://openalex.org/W3101960328","https://openalex.org/W1514481392","https://openalex.org/W2147599942","https://openalex.org/W4322770021","https://openalex.org/W2971149938","https://openalex.org/W2020502833","https://openalex.org/W2244793131","https://openalex.org/W3203194254"],"abstract_inverted_index":{"Difference":[0],"approximations":[1],"are":[2,32,48,80,99,127,145],"derived":[3,49,108],"for":[4,34,50,82],"the":[5,26,29,35,40,44,68,75,83,87,96,110,117,125,131,137,149,154],"second":[6,53,71],"order":[7,23,54,65,72],"wave":[8],"equation":[9],"in":[10,67,91],"one":[11],"and":[12,28,43,70,95,151],"two":[13],"space":[14],"dimensions,":[15],"without":[16],"first":[17,22],"writing":[18],"it":[19],"as":[20,57,59],"a":[21,51,60,92],"system.":[24],"Both":[25],"Dirichlet":[27,84],"Neumann":[30],"problems":[31],"treated":[33,128],"one-dimensional":[36],"case.":[37],"Relations":[38],"between":[39],"boundary":[41,97,126],"error":[42,47],"interior":[45,69,118],"phase":[46],"fully":[52],"accurate":[55,66,73],"discretization":[56,119],"well":[58],"scheme":[61,106,133],"that":[62],"is":[63,89,107,113,141],"fourth":[64],"at":[74],"boundary.":[76],"General":[77],"two-dimensional":[78],"domains":[79],"considered":[81],"problem":[85],"where":[86,109],"domain":[88],"embedded":[90],"Cartesian":[93],"grid":[94],"conditions":[98],"approximated":[100],"by":[101,116,124],"interpolation.":[102],"A":[103],"stable":[104],"conservative":[105],"time":[111],"step":[112],"determined":[114],"only":[115,140],"formula.":[120],"Discretization":[121],"cells":[122],"cut":[123],"implicitly,":[129],"but":[130],"resulting":[132],"becomes":[134],"explicit":[135],"because":[136],"implicit":[138],"dependence":[139],"pointwise.":[142],"Numerical":[143],"examples":[144],"provided":[146],"to":[147],"verify":[148],"stability":[150],"accuracy":[152],"of":[153],"proposed":[155],"method.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":14},{"year":2015,"cited_by_count":6},{"year":2014,"cited_by_count":4},{"year":2012,"cited_by_count":9}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}