{"id":"https://openalex.org/W2119372460","doi":"https://doi.org/10.1007/s10208-002-0062-x","title":"Modulated Fourier Expansions of Highly Oscillatory Differential Equations","display_name":"Modulated Fourier Expansions of Highly Oscillatory Differential Equations","publication_year":2003,"publication_date":"2003-02-07","ids":{"openalex":"https://openalex.org/W2119372460","doi":"https://doi.org/10.1007/s10208-002-0062-x","mag":"2119372460"},"language":"en","primary_location":{"id":"doi:10.1007/s10208-002-0062-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-002-0062-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-002-0062-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/s10208-002-0062-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047697581","display_name":"David Cohen","orcid":"https://orcid.org/0000-0001-6490-1957"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"David Cohen","raw_affiliation_strings":["Section de Math\u00e9matiques\n2-4, rue du Li\u00e9vre,\nCH-1211 Gen\u00e9ve 24, Switzerland","Section de Math\u00e9matiques#N#2-4, rue du Li\u00e9vre,#N#CH-1211 Gen\u00e9ve 24"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section de Math\u00e9matiques\n2-4, rue du Li\u00e9vre,\nCH-1211 Gen\u00e9ve 24, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Section de Math\u00e9matiques#N#2-4, rue du Li\u00e9vre,#N#CH-1211 Gen\u00e9ve 24","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026173495","display_name":"Ernst Hairer","orcid":"https://orcid.org/0000-0001-5057-2654"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"Ernst Hairer","raw_affiliation_strings":["Section de Math\u00e9matiques\n2-4, rue du Li\u00e9vre,\nCH-1211 Gen\u00e9ve 24, Switzerland","Section de Math\u00e9matiques#N#2-4, rue du Li\u00e9vre,#N#CH-1211 Gen\u00e9ve 24"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section de Math\u00e9matiques\n2-4, rue du Li\u00e9vre,\nCH-1211 Gen\u00e9ve 24, Switzerland","institution_ids":["https://openalex.org/I114457229"]},{"raw_affiliation_string":"Section de Math\u00e9matiques#N#2-4, rue du Li\u00e9vre,#N#CH-1211 Gen\u00e9ve 24","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["Universit\u00e4t T\u00fcbingen,\nMathematisches Institut,\nAuf der Morgenstelle 10,\nD-72076 T\u00fcbingen, Germany","Universit\u00e4t T\u00fcbingen,#N#Mathematisches Institut,#N#Auf der Morgenstelle 10,#N#D-72076 T\u00fcbingen"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen,\nMathematisches Institut,\nAuf der Morgenstelle 10,\nD-72076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]},{"raw_affiliation_string":"Universit\u00e4t T\u00fcbingen,#N#Mathematisches Institut,#N#Auf der Morgenstelle 10,#N#D-72076 T\u00fcbingen","institution_ids":["https://openalex.org/I8087733"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026173495","https://openalex.org/A5047697581","https://openalex.org/A5065792988"],"corresponding_institution_ids":["https://openalex.org/I114457229","https://openalex.org/I8087733"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":2.8269,"has_fulltext":true,"cited_by_count":64,"citation_normalized_percentile":{"value":0.91010499,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"3","issue":"4","first_page":"327","last_page":"345"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998000264167786,"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":0.9998000264167786,"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/T11261","display_name":"Quantum chaos and dynamical systems","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11575","display_name":"Nonlinear Photonic Systems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7504289746284485},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.684677004814148},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.646391749382019},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.6174430251121521},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6032673716545105},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.5876306891441345},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5455240607261658},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5388647317886353},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4611217677593231},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.42779308557510376},{"id":"https://openalex.org/keywords/harmonic-analysis","display_name":"Harmonic analysis","score":0.4129316806793213},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3810083568096161},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.23019501566886902},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10915100574493408},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08896443247795105}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7504289746284485},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.684677004814148},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.646391749382019},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.6174430251121521},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6032673716545105},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.5876306891441345},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5455240607261658},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5388647317886353},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4611217677593231},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42779308557510376},{"id":"https://openalex.org/C131770355","wikidata":"https://www.wikidata.org/wiki/Q876215","display_name":"Harmonic analysis","level":2,"score":0.4129316806793213},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3810083568096161},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.23019501566886902},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10915100574493408},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08896443247795105}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s10208-002-0062-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-002-0062-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-002-0062-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:unige.ch:unige:12279","is_oa":true,"landing_page_url":"https://archive-ouverte.unige.ch/unige:12279","pdf_url":null,"source":{"id":"https://openalex.org/S4306402259","display_name":"Archive ouverte UNIGE (University of Geneva)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I114457229","host_organization_name":"University of Geneva","host_organization_lineage":["https://openalex.org/I114457229"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 1615-3375","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.545.7596","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.545.7596","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.unige.ch/~hairer/preprints/FOCM3n4p327.pdf","raw_type":"text"},{"id":"pmh:oai:research.chalmers.se:516767","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/516767","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s10208-002-0062-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10208-002-0062-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10208-002-0062-x.pdf","source":{"id":"https://openalex.org/S151639445","display_name":"Foundations of Computational Mathematics","issn_l":"1615-3375","issn":["1615-3375","1615-3383"],"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":"Foundations of Computational Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.75,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2119372460.pdf","grobid_xml":"https://content.openalex.org/works/W2119372460.grobid-xml"},"referenced_works_count":9,"referenced_works":["https://openalex.org/W1544770838","https://openalex.org/W2011748668","https://openalex.org/W2043913140","https://openalex.org/W2046912058","https://openalex.org/W2053901685","https://openalex.org/W2071844352","https://openalex.org/W2084486264","https://openalex.org/W2128876821","https://openalex.org/W4240834412"],"related_works":["https://openalex.org/W2094684004","https://openalex.org/W4224306892","https://openalex.org/W1574935133","https://openalex.org/W2568904611","https://openalex.org/W31830636","https://openalex.org/W2370547058","https://openalex.org/W6842695","https://openalex.org/W2331443874","https://openalex.org/W4298260447","https://openalex.org/W1990381924"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":3}],"updated_date":"2026-08-08T07:41:36.138363","created_date":"2025-10-10T00:00:00"}
