{"id":"https://openalex.org/W2165959316","doi":"https://doi.org/10.1007/3-540-62598-4_123","title":"Grid approximations of the solution and diffusion flux for singularly perturbed equations with Neumann boundary conditions","display_name":"Grid approximations of the solution and diffusion flux for singularly perturbed equations with Neumann boundary conditions","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W2165959316","doi":"https://doi.org/10.1007/3-540-62598-4_123","mag":"2165959316"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-62598-4_123","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-62598-4_123","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/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"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Grigorii I. Shishkin","raw_affiliation_strings":["Institute of Mathematics and Mechanics, Ural Branch of Russian Acad. Sci., 16 S.Kovalevskoi Street, 620219, Ekaterinburg, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics and Mechanics, Ural Branch of Russian Acad. Sci., 16 S.Kovalevskoi Street, 620219, Ekaterinburg, Russia","institution_ids":["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"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":1.4843,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.8537234,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"430","last_page":"441"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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":1.0,"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":0.9839000105857849,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9731000065803528,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8249390125274658},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.6332111358642578},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5608542561531067},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5575620532035828},{"id":"https://openalex.org/keywords/rectangle","display_name":"Rectangle","score":0.5549670457839966},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5440447330474854},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5078077912330627},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.46261197328567505},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.41434240341186523},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.22726163268089294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1404041349887848}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8249390125274658},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6332111358642578},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5608542561531067},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5575620532035828},{"id":"https://openalex.org/C2781302577","wikidata":"https://www.wikidata.org/wiki/Q209","display_name":"Rectangle","level":2,"score":0.5549670457839966},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5440447330474854},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5078077912330627},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.46261197328567505},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.41434240341186523},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.22726163268089294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1404041349887848},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-62598-4_123","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-62598-4_123","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W1480673526","https://openalex.org/W2036371403","https://openalex.org/W2057967242","https://openalex.org/W2072685235","https://openalex.org/W2588200798","https://openalex.org/W4241946322"],"related_works":["https://openalex.org/W2242098268","https://openalex.org/W4244945894","https://openalex.org/W4224881918","https://openalex.org/W2003462717","https://openalex.org/W2802042052","https://openalex.org/W174828583","https://openalex.org/W1987609185","https://openalex.org/W2321986606","https://openalex.org/W2006251942","https://openalex.org/W3194042852"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}