{"id":"https://openalex.org/W2020238732","doi":"https://doi.org/10.2478/cmam-2009-0006","title":"Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity","display_name":"Numerical Method for Singularly Perturbed Parabolic Equations in Unbounded Domains in the Case of Solutions Growing at Infinity","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W2020238732","doi":"https://doi.org/10.2478/cmam-2009-0006","mag":"2020238732"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2009-0006","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0006","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0006/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0006/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091103112","display_name":"G. I. Shishkin","orcid":"https://orcid.org/0000-0002-6886-8979"},"institutions":[{"id":"https://openalex.org/I4210105350","display_name":"N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/029fhmb28","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210105350","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I4210119369","display_name":"Ural Branch of the Russian Academy of Sciences","ror":"https://ror.org/02s4h3z39","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210119369"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"G. I. Shishkin","raw_affiliation_strings":["1Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S.Kovalevskaya Str., 620219 Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"1Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S.Kovalevskaya Str., 620219 Ekaterinburg, Russia","institution_ids":["https://openalex.org/I4210119369","https://openalex.org/I4210105350"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5091103112"],"corresponding_institution_ids":["https://openalex.org/I4210105350","https://openalex.org/I4210119369"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.12134369,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"9","issue":"1","first_page":"100","last_page":"110"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9998999834060669,"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/T12727","display_name":"Differential Equations and Numerical Methods","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/T13685","display_name":"Material Science and Thermodynamics","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9710000157356262,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.8098664283752441},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.7134947776794434},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5947698354721069},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5917912125587463},{"id":"https://openalex.org/keywords/neighbourhood","display_name":"Neighbourhood (mathematics)","score":0.5488470792770386},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4735875725746155},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4430937170982361},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2161412537097931}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8098664283752441},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.7134947776794434},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5947698354721069},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5917912125587463},{"id":"https://openalex.org/C161677786","wikidata":"https://www.wikidata.org/wiki/Q2478475","display_name":"Neighbourhood (mathematics)","level":2,"score":0.5488470792770386},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4735875725746155},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4430937170982361},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2161412537097931},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.2478/cmam-2009-0006","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0006","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0006/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/cmam-2009-0006","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0006","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0006/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.5,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[{"id":"https://openalex.org/G5823188334","display_name":null,"funder_award_id":"06/MI/005","funder_id":"https://openalex.org/F4320320847","funder_display_name":"Science Foundation Ireland"}],"funders":[{"id":"https://openalex.org/F4320311521","display_name":"National University of Ireland","ror":"https://ror.org/00shsf120"},{"id":"https://openalex.org/F4320320847","display_name":"Science Foundation Ireland","ror":"https://ror.org/0271asj38"},{"id":"https://openalex.org/F4320321079","display_name":"Russian Foundation for Basic Research","ror":"https://ror.org/02mh1ke95"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2020238732.pdf","grobid_xml":"https://content.openalex.org/works/W2020238732.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W577555718","https://openalex.org/W1476132770","https://openalex.org/W1985037001","https://openalex.org/W2055656318","https://openalex.org/W2058102421","https://openalex.org/W2080753637","https://openalex.org/W2087837487","https://openalex.org/W2159904878","https://openalex.org/W2588200798","https://openalex.org/W4240371954","https://openalex.org/W4241946322","https://openalex.org/W4252111318","https://openalex.org/W4299292325"],"related_works":["https://openalex.org/W4248744973","https://openalex.org/W4383700488","https://openalex.org/W3037015124","https://openalex.org/W3021699323","https://openalex.org/W4287780535","https://openalex.org/W2959025308","https://openalex.org/W2129100545","https://openalex.org/W1972922485","https://openalex.org/W2001488143","https://openalex.org/W2392492385"],"abstract_inverted_index":{"Abstract":[0],"An":[1],"initial-boundary":[2,78],"value":[3,79],"problem":[4,80],"is":[5,86],"considered":[6],"in":[7,34,53,95,109],"an":[8],"unbounded":[9],"do-":[10],"main":[11],"on":[12],"the":[13,26,38,42,47,54,65,69,72,77,89,99,110],"x-axis":[14],"for":[15,61],"a":[16,29,35,50,96,102],"singularly":[17],"perturbed":[18],"parabolic":[19,30],"reaction-diffusion":[20],"equation.":[21],"For":[22],"small":[23],"values":[24,63],"of":[25,37,41,49,64,74,76,82,91,98],"parameter":[27,66],"\u03b5,":[28],"boundary":[31,100],"layer":[32],"arises":[33],"neighbourhood":[36,97],"lateral":[39],"part":[40],"boundary.":[43],"In":[44,68],"this":[45],"problem,":[46],"error":[48],"discrete":[51],"solution":[52],"maximum":[55,112],"norm":[56,113],"grows":[57],"without":[58],"bound":[59],"even":[60],"fixed":[62],"\u03b5.":[67],"present":[70],"paper,":[71],"proximity":[73],"solutions":[75],"and":[81],"its":[83],"numerical":[84],"approximations":[85],"considered.":[87],"Using":[88],"method":[90],"special":[92,103],"grids":[93],"condensing":[94],"layer,":[101],"finite":[104],"difference":[105],"scheme":[106],"converging":[107],"\u03b5-uniformly":[108],"weight":[111],"has":[114],"been":[115],"constructed.":[116]},"counts_by_year":[],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}