{"id":"https://openalex.org/W2057721195","doi":"https://doi.org/10.1007/s00211-005-0617-2","title":"Asymptotically correct error estimation for collocation methods applied to singular boundary value problems","display_name":"Asymptotically correct error estimation for collocation methods applied to singular boundary value problems","publication_year":2005,"publication_date":"2005-05-31","ids":{"openalex":"https://openalex.org/W2057721195","doi":"https://doi.org/10.1007/s00211-005-0617-2","mag":"2057721195"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-005-0617-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-005-0617-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5056549733","display_name":"Othmar Koch","orcid":"https://orcid.org/0000-0002-1956-221X"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Othmar Koch","raw_affiliation_strings":["Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria","Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8\u201310, 1040 Wien, Austria"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institute for Analysis and Scientific Computing, Vienna University of Technology, Wiedner Hauptstrasse 8\u201310, 1040 Wien, Austria","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5056549733"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":3.2886,"has_fulltext":false,"cited_by_count":37,"citation_normalized_percentile":{"value":0.92238435,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"101","issue":"1","first_page":"143","last_page":"164"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9980000257492065,"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/mathematics","display_name":"Mathematics","score":0.8806334733963013},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.7232586741447449},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6666582822799683},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5826259851455688},{"id":"https://openalex.org/keywords/singularity","display_name":"Singularity","score":0.5725880861282349},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5627296566963196},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5336324572563171},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.5326741933822632},{"id":"https://openalex.org/keywords/singular-value-decomposition","display_name":"Singular value decomposition","score":0.4968314468860626},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4898638427257538},{"id":"https://openalex.org/keywords/correctness","display_name":"Correctness","score":0.47150057554244995},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.47051042318344116},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45653921365737915},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.44064250588417053},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.43572917580604553},{"id":"https://openalex.org/keywords/singular-solution","display_name":"Singular solution","score":0.41866278648376465},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4108723998069763},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4055209457874298},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3273303508758545},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.12921792268753052},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.12701159715652466},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08749914169311523}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8806334733963013},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.7232586741447449},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6666582822799683},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5826259851455688},{"id":"https://openalex.org/C16171025","wikidata":"https://www.wikidata.org/wiki/Q863349","display_name":"Singularity","level":2,"score":0.5725880861282349},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5627296566963196},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5336324572563171},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.5326741933822632},{"id":"https://openalex.org/C22789450","wikidata":"https://www.wikidata.org/wiki/Q420904","display_name":"Singular value decomposition","level":2,"score":0.4968314468860626},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4898638427257538},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.47150057554244995},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.47051042318344116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45653921365737915},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.44064250588417053},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.43572917580604553},{"id":"https://openalex.org/C135909967","wikidata":"https://www.wikidata.org/wiki/Q4338245","display_name":"Singular solution","level":2,"score":0.41866278648376465},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4108723998069763},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4055209457874298},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3273303508758545},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.12921792268753052},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.12701159715652466},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08749914169311523},{"id":"https://openalex.org/C127313418","wikidata":"https://www.wikidata.org/wiki/Q1069","display_name":"Geology","level":0,"score":0.0},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C62649853","wikidata":"https://www.wikidata.org/wiki/Q199687","display_name":"Remote sensing","level":1,"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":1,"locations":[{"id":"doi:10.1007/s00211-005-0617-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-005-0617-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.4699999988079071,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W14803345","https://openalex.org/W1969634399","https://openalex.org/W1971092129","https://openalex.org/W1971947347","https://openalex.org/W1973937820","https://openalex.org/W1980770629","https://openalex.org/W1983952517","https://openalex.org/W2003585698","https://openalex.org/W2014289408","https://openalex.org/W2014511801","https://openalex.org/W2027382177","https://openalex.org/W2028653043","https://openalex.org/W2029604183","https://openalex.org/W2044751500","https://openalex.org/W2054822287","https://openalex.org/W2056645185","https://openalex.org/W2061097835","https://openalex.org/W2063252778","https://openalex.org/W2067265108","https://openalex.org/W2080819158","https://openalex.org/W2090579867","https://openalex.org/W2117432795","https://openalex.org/W2144828711","https://openalex.org/W2147704408","https://openalex.org/W2150208829","https://openalex.org/W2171369888","https://openalex.org/W2325916166","https://openalex.org/W2990299855","https://openalex.org/W4298334204"],"related_works":["https://openalex.org/W2068202711","https://openalex.org/W3038241949","https://openalex.org/W3021297805","https://openalex.org/W3093556794","https://openalex.org/W28631575","https://openalex.org/W2505315915","https://openalex.org/W2172162055","https://openalex.org/W631163165","https://openalex.org/W1992210319","https://openalex.org/W2057721195"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}