{"id":"https://openalex.org/W1972053220","doi":"https://doi.org/10.1007/s11075-009-9280-5","title":"Two-step almost collocation methods for ordinary differential equations","display_name":"Two-step almost collocation methods for ordinary differential equations","publication_year":2009,"publication_date":"2009-03-16","ids":{"openalex":"https://openalex.org/W1972053220","doi":"https://doi.org/10.1007/s11075-009-9280-5","mag":"1972053220"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-009-9280-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-009-9280-5","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","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/A5087607360","display_name":"Raffaele D\u2019Ambrosio","orcid":"https://orcid.org/0000-0001-5178-5416"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"R. D\u2019Ambrosio","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e1 di Salerno, Fisciano, Salerno, 84084, Italy","Universit\u00e1 di Salerno"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e1 di Salerno, Fisciano, Salerno, 84084, Italy","institution_ids":["https://openalex.org/I131729948"]},{"raw_affiliation_string":"Universit\u00e1 di Salerno","institution_ids":["https://openalex.org/I131729948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014614796","display_name":"Matteo Ferro","orcid":"https://orcid.org/0000-0002-9250-7858"},"institutions":[{"id":"https://openalex.org/I71267560","display_name":"University of Naples Federico II","ror":"https://ror.org/05290cv24","country_code":"IT","type":"education","lineage":["https://openalex.org/I71267560"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"M. Ferro","raw_affiliation_strings":["Dipartimento di Matematica e Applicazioni, Universit\u00e1 di Napoli - \u201cFederico II\u201d, 80126, Napoli, Italy","Universit\u00e1 di Napoli - \u201cFederico II\u201d"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Applicazioni, Universit\u00e1 di Napoli - \u201cFederico II\u201d, 80126, Napoli, Italy","institution_ids":["https://openalex.org/I71267560"]},{"raw_affiliation_string":"Universit\u00e1 di Napoli - \u201cFederico II\u201d","institution_ids":["https://openalex.org/I71267560"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011860849","display_name":"Z. Jackiewicz","orcid":"https://orcid.org/0000-0002-9823-3042"},"institutions":[{"id":"https://openalex.org/I55732556","display_name":"Arizona State University","ror":"https://ror.org/03efmqc40","country_code":"US","type":"education","lineage":["https://openalex.org/I55732556"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Z. Jackiewicz","raw_affiliation_strings":["Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA","Arizona State University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Arizona State University, Tempe, AZ, 85287, USA","institution_ids":["https://openalex.org/I55732556"]},{"raw_affiliation_string":"Arizona State University","institution_ids":["https://openalex.org/I55732556"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082093853","display_name":"Beatrice Paternoster","orcid":"https://orcid.org/0000-0002-9712-1364"},"institutions":[{"id":"https://openalex.org/I131729948","display_name":"University of Salerno","ror":"https://ror.org/0192m2k53","country_code":"IT","type":"education","lineage":["https://openalex.org/I131729948"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"B. Paternoster","raw_affiliation_strings":["Dipartimento di Matematica e Informatica, Universit\u00e1 di Salerno, Fisciano, Salerno, 84084, Italy","Universit\u00e1 di Salerno"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Dipartimento di Matematica e Informatica, Universit\u00e1 di Salerno, Fisciano, Salerno, 84084, Italy","institution_ids":["https://openalex.org/I131729948"]},{"raw_affiliation_string":"Universit\u00e1 di Salerno","institution_ids":["https://openalex.org/I131729948"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087607360"],"corresponding_institution_ids":["https://openalex.org/I131729948"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":4.9125,"has_fulltext":false,"cited_by_count":49,"citation_normalized_percentile":{"value":0.95732839,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"53","issue":"2-3","first_page":"195","last_page":"217"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","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/T11416","display_name":"Numerical methods for differential equations","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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9984999895095825,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9983999729156494,"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/collocation-method","display_name":"Collocation method","score":0.9002499580383301},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8151094913482666},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.8025387525558472},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7944941520690918},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.7431883811950684},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6748200058937073},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6032586693763733},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.5937201380729675},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48761239647865295},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.4829391837120056},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4782601594924927},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45964598655700684},{"id":"https://openalex.org/keywords/l-stability","display_name":"L-stability","score":0.4509430229663849},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38521134853363037},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38402408361434937},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12811064720153809},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.11560499668121338}],"concepts":[{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.9002499580383301},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8151094913482666},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.8025387525558472},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7944941520690918},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7431883811950684},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6748200058937073},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6032586693763733},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.5937201380729675},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48761239647865295},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.4829391837120056},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4782601594924927},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45964598655700684},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.4509430229663849},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38521134853363037},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38402408361434937},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12811064720153809},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.11560499668121338},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-009-9280-5","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-009-9280-5","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W2721161","https://openalex.org/W51374244","https://openalex.org/W1543750907","https://openalex.org/W1555459452","https://openalex.org/W1576783654","https://openalex.org/W1596150805","https://openalex.org/W1620581513","https://openalex.org/W1967697356","https://openalex.org/W1969944682","https://openalex.org/W1973469783","https://openalex.org/W1976213300","https://openalex.org/W1985004680","https://openalex.org/W1991214860","https://openalex.org/W1994213792","https://openalex.org/W1996454905","https://openalex.org/W2000531430","https://openalex.org/W2009514289","https://openalex.org/W2010179730","https://openalex.org/W2015736664","https://openalex.org/W2041934546","https://openalex.org/W2044282524","https://openalex.org/W2068711724","https://openalex.org/W2092811961","https://openalex.org/W2111358340","https://openalex.org/W2138301603","https://openalex.org/W2334068286","https://openalex.org/W2480201659","https://openalex.org/W2914660408","https://openalex.org/W2981569720","https://openalex.org/W2997123088","https://openalex.org/W4292929576","https://openalex.org/W4300831640"],"related_works":["https://openalex.org/W2136451125","https://openalex.org/W1843663759","https://openalex.org/W2378531610","https://openalex.org/W832825236","https://openalex.org/W2956395387","https://openalex.org/W181143595","https://openalex.org/W2088005785","https://openalex.org/W2373806316","https://openalex.org/W2027444793","https://openalex.org/W2040892753"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"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":5},{"year":2012,"cited_by_count":5}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2025-10-10T00:00:00"}