{"id":"https://openalex.org/W1994902252","doi":"https://doi.org/10.1137/s0036142999358743","title":"Numerical Solution of Non--Self-Adjoint Sturm--Liouville Problems and Related Systems","display_name":"Numerical Solution of Non--Self-Adjoint Sturm--Liouville Problems and Related Systems","publication_year":2001,"publication_date":"2001-01-01","ids":{"openalex":"https://openalex.org/W1994902252","doi":"https://doi.org/10.1137/s0036142999358743","mag":"1994902252"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142999358743","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999358743","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/A5074699388","display_name":"Leon A. Greenberg","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Leon Greenberg","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5039382364","display_name":"Marco Marletta","orcid":null},"institutions":[{"id":"https://openalex.org/I153648349","display_name":"University of Leicester","ror":"https://ror.org/04h699437","country_code":"GB","type":"education","lineage":["https://openalex.org/I153648349"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Marco Marletta","raw_affiliation_strings":["University of Leicester"],"affiliations":[{"raw_affiliation_string":"University of Leicester","institution_ids":["https://openalex.org/I153648349"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5074699388"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.8947,"has_fulltext":false,"cited_by_count":36,"citation_normalized_percentile":{"value":0.92944957,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"38","issue":"6","first_page":"1800","last_page":"1845"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.998199999332428,"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"}},{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9973999857902527,"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/sturm\u2013liouville-theory","display_name":"Sturm\u2013Liouville theory","score":0.9177078604698181},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8841356039047241},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.8451870083808899},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.6304309964179993},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.5904877185821533},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5749099254608154},{"id":"https://openalex.org/keywords/matrix-differential-equation","display_name":"Matrix differential equation","score":0.5191770792007446},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5035662055015564},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4915235936641693},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.47294995188713074},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4666447937488556},{"id":"https://openalex.org/keywords/complex-plane","display_name":"Complex plane","score":0.4562787115573883},{"id":"https://openalex.org/keywords/self-adjoint-operator","display_name":"Self-adjoint operator","score":0.44540679454803467},{"id":"https://openalex.org/keywords/plane","display_name":"Plane (geometry)","score":0.4327777624130249},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4259111285209656},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.23143133521080017},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.13746660947799683},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.09770047664642334}],"concepts":[{"id":"https://openalex.org/C22892174","wikidata":"https://www.wikidata.org/wiki/Q1154082","display_name":"Sturm\u2013Liouville theory","level":3,"score":0.9177078604698181},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8841356039047241},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.8451870083808899},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.6304309964179993},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5904877185821533},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5749099254608154},{"id":"https://openalex.org/C105671362","wikidata":"https://www.wikidata.org/wiki/Q6787870","display_name":"Matrix differential equation","level":3,"score":0.5191770792007446},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5035662055015564},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4915235936641693},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.47294995188713074},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4666447937488556},{"id":"https://openalex.org/C179117685","wikidata":"https://www.wikidata.org/wiki/Q328998","display_name":"Complex plane","level":2,"score":0.4562787115573883},{"id":"https://openalex.org/C171972299","wikidata":"https://www.wikidata.org/wiki/Q6500908","display_name":"Self-adjoint operator","level":3,"score":0.44540679454803467},{"id":"https://openalex.org/C17825722","wikidata":"https://www.wikidata.org/wiki/Q17285","display_name":"Plane (geometry)","level":2,"score":0.4327777624130249},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4259111285209656},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.23143133521080017},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.13746660947799683},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.09770047664642334},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"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/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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":2,"locations":[{"id":"doi:10.1137/s0036142999358743","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142999358743","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:10.1.1.22.7095","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.22.7095","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/~lng/slnsa.ps","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W26725264","https://openalex.org/W1489216560","https://openalex.org/W1498751840","https://openalex.org/W1537906002","https://openalex.org/W1552454956","https://openalex.org/W1624156688","https://openalex.org/W1982421284","https://openalex.org/W1984814586","https://openalex.org/W1985433917","https://openalex.org/W1998127757","https://openalex.org/W2001772722","https://openalex.org/W2002882065","https://openalex.org/W2006346854","https://openalex.org/W2013521517","https://openalex.org/W2039601065","https://openalex.org/W2039763880","https://openalex.org/W2044315243","https://openalex.org/W2047370137","https://openalex.org/W2051965379","https://openalex.org/W2053874515","https://openalex.org/W2055931342","https://openalex.org/W2062595625","https://openalex.org/W2062864779","https://openalex.org/W2067377180","https://openalex.org/W2070793107","https://openalex.org/W2078634887","https://openalex.org/W2079628376","https://openalex.org/W2080585605","https://openalex.org/W2083197540","https://openalex.org/W2087645512","https://openalex.org/W2130630106","https://openalex.org/W2130727150","https://openalex.org/W2141320665","https://openalex.org/W2141981259","https://openalex.org/W2314840837","https://openalex.org/W2338448110","https://openalex.org/W2798909945","https://openalex.org/W2914912151","https://openalex.org/W2970105038","https://openalex.org/W4205196489"],"related_works":["https://openalex.org/W4361225129","https://openalex.org/W2093769064","https://openalex.org/W2068890958","https://openalex.org/W2025337698","https://openalex.org/W1964991417","https://openalex.org/W2064918658","https://openalex.org/W2137506121","https://openalex.org/W1996725259","https://openalex.org/W1986242508","https://openalex.org/W1988140364"],"abstract_inverted_index":{"This":[0],"paper":[1],"gives":[2],"the":[3,13,34,46,50,55,61,81,84,87,94,101,112],"analysis":[4],"and":[5,39,115],"numerics":[6],"underlying":[7],"a":[8,37,41,73,104],"shooting":[9],"method":[10,31,53,108],"for":[11,89],"approximating":[12],"eigenvalues":[14,35,102],"of":[15,64,83,86,93],"non--self-adjoint":[16],"Sturm--Liouville":[17,77],"problems.":[18],"We":[19,79],"consider":[20],"even":[21],"order":[22,75,98],"problems":[23],"with":[24,49],"(equally":[25],"divided)":[26],"separated":[27],"boundary":[28],"conditions.":[29],"The":[30,107],"can":[32,67],"find":[33],"in":[36,40,97,103],"rectangle":[38],"left":[42,105],"half-plane.":[43,106],"It":[44],"combines":[45],"argument":[47],"principle":[48],"compound":[51,65],"matrix":[52],"(using":[54],"Magnus":[56],"expansion).":[57],"In":[58],"some":[59],"cases":[60],"computational":[62],"cost":[63],"matrices":[66],"be":[68],"reduced":[69],"by":[70],"transforming":[71],"to":[72,99,111],"second":[74],"vector":[76],"problem.":[78],"study":[80],"asymptotics":[82],"solutions":[85],"ODE":[88],"large":[90],"absolute":[91],"values":[92],"eigenvalue":[95],"parameter":[96],"calculate":[100],"is":[109],"applied":[110],"Orr--Sommerfeld":[113],"equation":[114],"other":[116],"examples.":[117]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
