{"id":"https://openalex.org/W1996756530","doi":"https://doi.org/10.1090/s0025-5718-99-01034-0","title":"On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations","display_name":"On best possible order of convergence estimates in the collocation method and Galerkin's method for singularly perturbed boundary value problems for systems of first-order ordinary differential equations","publication_year":1999,"publication_date":"1999-04-01","ids":{"openalex":"https://openalex.org/W1996756530","doi":"https://doi.org/10.1090/s0025-5718-99-01034-0","mag":"1996756530"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-99-01034-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01034-0","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01034-0/S0025-5718-99-01034-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01034-0/S0025-5718-99-01034-0.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036989241","display_name":"I. A. Blatov","orcid":"https://orcid.org/0000-0001-6215-8311"},"institutions":[{"id":"https://openalex.org/I71305448","display_name":"Voronezh State University","ror":"https://ror.org/0543j5e78","country_code":"RU","type":"education","lineage":["https://openalex.org/I71305448"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"I. A. Blatov","raw_affiliation_strings":["Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693","institution_ids":["https://openalex.org/I71305448"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010054911","display_name":"V. V. Strygin","orcid":null},"institutions":[{"id":"https://openalex.org/I71305448","display_name":"Voronezh State University","ror":"https://ror.org/0543j5e78","country_code":"RU","type":"education","lineage":["https://openalex.org/I71305448"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"V. V. Strygin","raw_affiliation_strings":["Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics and Mechanics, Voronezh State University, Universitetskaya pl.1, Voronezh, Russia, 394693","institution_ids":["https://openalex.org/I71305448"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5036989241"],"corresponding_institution_ids":["https://openalex.org/I71305448"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.15397083,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"68","issue":"226","first_page":"683","last_page":"716"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9962000250816345,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9957000017166138,"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":0.914901852607727},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7262343168258667},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.7010602951049805},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6542126536369324},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.6248420476913452},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6069719791412354},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5440217852592468},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4799613952636719},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4667786657810211},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4573300778865814},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44876620173454285},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4118127226829529},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.302324116230011},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.16987216472625732}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.914901852607727},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7262343168258667},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.7010602951049805},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6542126536369324},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6248420476913452},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6069719791412354},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5440217852592468},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4799613952636719},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4667786657810211},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4573300778865814},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44876620173454285},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4118127226829529},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.302324116230011},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.16987216472625732},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","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},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"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/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-99-01034-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01034-0","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01034-0/S0025-5718-99-01034-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-99-01034-0","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-99-01034-0","pdf_url":"https://www.ams.org/mcom/1999-68-226/S0025-5718-99-01034-0/S0025-5718-99-01034-0.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1996756530.pdf","grobid_xml":"https://content.openalex.org/works/W1996756530.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W105661347","https://openalex.org/W410026136","https://openalex.org/W1971092129","https://openalex.org/W1989828297","https://openalex.org/W2004492379","https://openalex.org/W2005171998","https://openalex.org/W2013553866","https://openalex.org/W2021015894","https://openalex.org/W2038872300","https://openalex.org/W2041523977","https://openalex.org/W2050434873","https://openalex.org/W2065279412","https://openalex.org/W2067115013","https://openalex.org/W2073195457","https://openalex.org/W2077952773","https://openalex.org/W2082621526","https://openalex.org/W2162870748","https://openalex.org/W3021722416","https://openalex.org/W4210300254","https://openalex.org/W4232120058","https://openalex.org/W4234694874","https://openalex.org/W4236932689","https://openalex.org/W4242863606","https://openalex.org/W4245170145"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W4255016916","https://openalex.org/W2078318892","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W124933011","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"The":[0],"collocation":[1,47],"method":[2,5,39,48],"and":[3],"Galerkin":[4,38],"using":[6],"parabolic":[7],"splines":[8],"are":[9,27,34,42,50],"considered.":[10],"Special":[11],"adaptive":[12],"meshes":[13],"whose":[14],"number":[15],"of":[16,20,24],"knots":[17],"is":[18],"independent":[19],"the":[21,25,32,37,46],"small":[22],"parameter":[23],"problem":[26],"used.":[28],"Unimprovable":[29],"estimates":[30,41],"in":[31],"$L_\\infty$-norm":[33],"obtained.":[35],"For":[36],"these":[40],"quasioptimal,":[43],"while":[44],"for":[45],"they":[49],"suboptimal.":[51]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
