{"id":"https://openalex.org/W2137308669","doi":"https://doi.org/10.1137/0153039","title":"Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems","display_name":"Summing Logarithmic Expansions for Singularly Perturbed Eigenvalue Problems","publication_year":1993,"publication_date":"1993-06-01","ids":{"openalex":"https://openalex.org/W2137308669","doi":"https://doi.org/10.1137/0153039","mag":"2137308669"},"language":"en","primary_location":{"id":"doi:10.1137/0153039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153039","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 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/A5037517718","display_name":"Michael J. Ward","orcid":"https://orcid.org/0000-0001-6959-7202"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Michael J. Ward","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5098330574","display_name":"William D. Heshaw","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"William D. Heshaw","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5108775680","display_name":"Joseph B. Keller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Joseph B. Keller","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5037517718"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.7482,"has_fulltext":false,"cited_by_count":141,"citation_normalized_percentile":{"value":0.91812564,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":99},"biblio":{"volume":"53","issue":"3","first_page":"799","last_page":"828"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9995999932289124,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.995199978351593,"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":0.7540072202682495},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7413742542266846},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.7078937888145447},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.6153835654258728},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.6144972443580627},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.5511995553970337},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4966443181037903},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.46957939863204956},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.45469987392425537},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.4510778486728668},{"id":"https://openalex.org/keywords/lambda","display_name":"Lambda","score":0.42372581362724304},{"id":"https://openalex.org/keywords/series-expansion","display_name":"Series expansion","score":0.41433268785476685},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.20226570963859558},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08222851157188416}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7540072202682495},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7413742542266846},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7078937888145447},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.6153835654258728},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.6144972443580627},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.5511995553970337},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4966443181037903},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.46957939863204956},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.45469987392425537},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.4510778486728668},{"id":"https://openalex.org/C2778113609","wikidata":"https://www.wikidata.org/wiki/Q10897","display_name":"Lambda","level":2,"score":0.42372581362724304},{"id":"https://openalex.org/C186080144","wikidata":"https://www.wikidata.org/wiki/Q358733","display_name":"Series expansion","level":2,"score":0.41433268785476685},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.20226570963859558},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08222851157188416},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0153039","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0153039","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1965171290","https://openalex.org/W1965991653","https://openalex.org/W2037622031","https://openalex.org/W2039941126","https://openalex.org/W2047898167","https://openalex.org/W2050434873","https://openalex.org/W2065932192","https://openalex.org/W2275931701","https://openalex.org/W2320678687","https://openalex.org/W2460205076","https://openalex.org/W3002379364","https://openalex.org/W4292917823"],"related_works":["https://openalex.org/W2806574890","https://openalex.org/W2235936547","https://openalex.org/W2004592678","https://openalex.org/W4240163599","https://openalex.org/W3009732457","https://openalex.org/W2071891167","https://openalex.org/W3122054165","https://openalex.org/W4233096695","https://openalex.org/W2012804516","https://openalex.org/W2470253477"],"abstract_inverted_index":{"Strong":[0],"localized":[1],"perturbations":[2],"of":[3,25,36,41,48,61,70,80,96,119,127,150,163,192],"linear":[4],"and":[5,28,54,83,122,172],"nonlinear":[6,38],"eigenvalue":[7,21,39],"problems":[8,89],"in":[9,94,147,177,208,237],"a":[10,37,43,56,112,151,178,182,232,238],"bounded":[11],"two-dimensional":[12],"domain":[13,239],"D":[14,53],"are":[15,65,204],"considered.":[16],"The":[17,219],"effects":[18],"on":[19,29,58,116,123,131],"an":[20],"$\\lambda":[22,33],"_0":[23],"$":[24,35,121],"the":[26,30,59,62,68,78,81,117,124,128,132,141,148,159,164,190,201,216,227],"Lapla-cian,":[27],"fold":[31,84],"point":[32],"_{c0}":[34],"problem,":[40],"removing":[42],"small":[44,245],"subdomain":[45],"$D_\\epsilon":[46,120],"$,":[47,51],"\u201cradius\u201d":[49],"$\\epsilon":[50],"from":[52,200],"imposing":[55],"condition":[57,130],"boundary":[60,129],"resulting":[63],"hole,":[64],"determined.":[66],"Using":[67],"method":[69,185,221],"matched":[71],"asymptotic":[72],"expansions,":[73],"it":[74,137],"is":[75,111,138,145,169,186,222],"shown":[76,139,205],"that":[77,114,140,155],"expansions":[79],"eigenvalues":[82],"points":[85],"for":[86,231],"these":[87,194],"perturbed":[88,217],"start":[90],"with":[91,211,240],"infinite":[92,143,195],"series":[93,144],"powers":[95],"$(":[97],"-":[98],"1/\\log":[99],"[":[100],"\\epsilon":[101],"d(":[102],"\\kappa":[103,109],")":[104],"]":[105],")$.":[106],"Here":[107],"$d(":[108],")$":[110],"constant":[113],"depends":[115],"shape":[118,162],"precise":[125],"form":[126],"hole.":[133,165],"In":[134],"each":[135],"case,":[136],"entire":[142],"contained":[146],"solution":[149],"single":[152],"related":[153,167],"problem":[154,168],"does":[156],"not":[157,170],"involve":[158],"size":[160],"or":[161],"This":[166],"stiff":[171],"can":[173],"be":[174,207],"solved":[175],"numerically":[176],"straightforward":[179],"way.":[180],"Thus":[181],"hybrid":[183,202,220],"asymptotic-numerical":[184],"obtained,":[187],"which":[188],"has":[189],"effect":[191],"summing":[193],"logarithmic":[196],"expansions.":[197],"Results":[198],"obtained":[199],"formulation":[203],"to":[206,215,225],"close":[209],"agreement":[210],"full":[212],"numerical":[213],"solutions":[214],"problems.":[218],"then":[223],"used":[224],"determine":[226],"absorption":[228],"time":[229],"distribution":[230],"particle":[233],"performing":[234],"Brownian":[235],"motion":[236],"reflecting":[241],"walls":[242],"containing":[243],"several":[244],"absorbing":[246],"obstacles.":[247]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":10},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":7},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
