{"id":"https://openalex.org/W2014200951","doi":"https://doi.org/10.1090/s0025-5718-07-01987-4","title":"An exponentially convergent algorithm for nonlinear differential equations in Banach spaces","display_name":"An exponentially convergent algorithm for nonlinear differential equations in Banach spaces","publication_year":2007,"publication_date":"2007-04-19","ids":{"openalex":"https://openalex.org/W2014200951","doi":"https://doi.org/10.1090/s0025-5718-07-01987-4","mag":"2014200951"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-07-01987-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01987-4","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01987-4/S0025-5718-07-01987-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","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":"hybrid","oa_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01987-4/S0025-5718-07-01987-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057130441","display_name":"I. P. Gavrilyuk","orcid":"https://orcid.org/0000-0003-3115-9690"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ivan Gavrilyuk","raw_affiliation_strings":["Staatliche Studienakademie Thueringen-Berufsakademie Eisenach, University of Cooperative Edukation, Am Wartenberg 2, D-99817 Eisenach, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Staatliche Studienakademie Thueringen-Berufsakademie Eisenach, University of Cooperative Edukation, Am Wartenberg 2, D-99817 Eisenach, Germany","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009476835","display_name":"\u0412. \u041b. \u041c\u0430\u043a\u0430\u0440\u043e\u0432","orcid":"https://orcid.org/0000-0002-4883-6574"},"institutions":[{"id":"https://openalex.org/I149851306","display_name":"National Academy of Sciences of Ukraine","ror":"https://ror.org/00je4t102","country_code":"UA","type":"government","lineage":["https://openalex.org/I149851306"]},{"id":"https://openalex.org/I190444043","display_name":"Institute of Mathematics","ror":"https://ror.org/04q3mp532","country_code":"UA","type":"facility","lineage":["https://openalex.org/I149851306","https://openalex.org/I190444043"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Volodymyr Makarov","raw_affiliation_strings":["National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschenkivska 3, 01601 Kiev, Ukraine","institution_ids":["https://openalex.org/I190444043","https://openalex.org/I149851306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5088,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65834306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"76","issue":"260","first_page":"1895","last_page":"1923"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9988999962806702,"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":0.9988999962806702,"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":0.9988999962806702,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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":0.9181674718856812},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.6302832365036011},{"id":"https://openalex.org/keywords/c0-semigroup","display_name":"C0-semigroup","score":0.601715624332428},{"id":"https://openalex.org/keywords/sinc-function","display_name":"Sinc function","score":0.5465559363365173},{"id":"https://openalex.org/keywords/compact-operator","display_name":"Compact operator","score":0.5403047800064087},{"id":"https://openalex.org/keywords/finite-rank-operator","display_name":"Finite-rank operator","score":0.5088432431221008},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.5046318769454956},{"id":"https://openalex.org/keywords/semi-elliptic-operator","display_name":"Semi-elliptic operator","score":0.4947924017906189},{"id":"https://openalex.org/keywords/approximation-property","display_name":"Approximation property","score":0.4556683301925659},{"id":"https://openalex.org/keywords/hypoelliptic-operator","display_name":"Hypoelliptic operator","score":0.45434874296188354},{"id":"https://openalex.org/keywords/hyperbola","display_name":"Hyperbola","score":0.44191455841064453},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.43922650814056396},{"id":"https://openalex.org/keywords/pseudo-monotone-operator","display_name":"Pseudo-monotone operator","score":0.427750825881958},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.41529595851898193},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.3807378113269806},{"id":"https://openalex.org/keywords/operator-space","display_name":"Operator space","score":0.18429851531982422}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9181674718856812},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.6302832365036011},{"id":"https://openalex.org/C19496378","wikidata":"https://www.wikidata.org/wiki/Q846542","display_name":"C0-semigroup","level":3,"score":0.601715624332428},{"id":"https://openalex.org/C152303783","wikidata":"https://www.wikidata.org/wiki/Q855949","display_name":"Sinc function","level":2,"score":0.5465559363365173},{"id":"https://openalex.org/C79013869","wikidata":"https://www.wikidata.org/wiki/Q1780743","display_name":"Compact operator","level":3,"score":0.5403047800064087},{"id":"https://openalex.org/C99392333","wikidata":"https://www.wikidata.org/wiki/Q5450385","display_name":"Finite-rank operator","level":3,"score":0.5088432431221008},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.5046318769454956},{"id":"https://openalex.org/C24902271","wikidata":"https://www.wikidata.org/wiki/Q7449297","display_name":"Semi-elliptic operator","level":3,"score":0.4947924017906189},{"id":"https://openalex.org/C152306953","wikidata":"https://www.wikidata.org/wiki/Q621744","display_name":"Approximation property","level":3,"score":0.4556683301925659},{"id":"https://openalex.org/C187123786","wikidata":"https://www.wikidata.org/wiki/Q4138816","display_name":"Hypoelliptic operator","level":4,"score":0.45434874296188354},{"id":"https://openalex.org/C145050668","wikidata":"https://www.wikidata.org/wiki/Q165301","display_name":"Hyperbola","level":2,"score":0.44191455841064453},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.43922650814056396},{"id":"https://openalex.org/C201040074","wikidata":"https://www.wikidata.org/wiki/Q7254436","display_name":"Pseudo-monotone operator","level":5,"score":0.427750825881958},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.41529595851898193},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.3807378113269806},{"id":"https://openalex.org/C176691602","wikidata":"https://www.wikidata.org/wiki/Q7097841","display_name":"Operator space","level":4,"score":0.18429851531982422},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-07-01987-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01987-4","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01987-4/S0025-5718-07-01987-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.154.2552","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.154.2552","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2007-76-260/S0025-5718-07-01987-4/S0025-5718-07-01987-4.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-07-01987-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-07-01987-4","pdf_url":"https://www.ams.org/mcom/2007-76-260/S0025-5718-07-01987-4/S0025-5718-07-01987-4.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":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2014200951.pdf","grobid_xml":"https://content.openalex.org/works/W2014200951.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W263866058","https://openalex.org/W628383724","https://openalex.org/W1516587486","https://openalex.org/W1527296550","https://openalex.org/W1560060148","https://openalex.org/W1586044118","https://openalex.org/W1983001687","https://openalex.org/W1984613947","https://openalex.org/W1995356931","https://openalex.org/W1998665522","https://openalex.org/W2009132071","https://openalex.org/W2011326283","https://openalex.org/W2012405708","https://openalex.org/W2014200951","https://openalex.org/W2024325396","https://openalex.org/W2028247581","https://openalex.org/W2030565709","https://openalex.org/W2031667286","https://openalex.org/W2035766380","https://openalex.org/W2047808645","https://openalex.org/W2055175862","https://openalex.org/W2060176450","https://openalex.org/W2062782716","https://openalex.org/W2070279765","https://openalex.org/W2090581346","https://openalex.org/W2123426570","https://openalex.org/W2156436556","https://openalex.org/W2330189039","https://openalex.org/W2408478130","https://openalex.org/W2970097143","https://openalex.org/W3038165843","https://openalex.org/W4293185733","https://openalex.org/W4298060601","https://openalex.org/W4301709274","https://openalex.org/W6680966031"],"related_works":["https://openalex.org/W2202672589","https://openalex.org/W2274500052","https://openalex.org/W2130696028","https://openalex.org/W2565275126","https://openalex.org/W2339884493","https://openalex.org/W2146485284","https://openalex.org/W2179261669","https://openalex.org/W2092933505","https://openalex.org/W3175776911","https://openalex.org/W70028720"],"abstract_inverted_index":{"An":[0],"exponentially":[1],"convergent":[2],"approximation":[3],"to":[4],"the":[5,34,39,55,58,63,69],"solution":[6],"of":[7,57],"a":[8,48,52],"nonlinear":[9],"first":[10],"order":[11],"differential":[12],"equation":[13,32],"with":[14],"an":[15,28,73],"operator":[16,35,40,43,59],"coefficient":[17],"in":[18],"Banach":[19],"space":[20],"is":[21,25,45],"proposed.":[22],"The":[23,42],"algorithm":[24],"based":[26],"on":[27],"equivalent":[29],"Volterra":[30],"integral":[31,50],"including":[33],"exponential":[36,44],"generated":[37],"by":[38,47],"coefficient.":[41],"represented":[46],"Dunford-Cauchy":[49],"along":[51],"hyperbola":[53],"enveloping":[54],"spectrum":[56],"coefficient,":[60],"and":[61,72],"then":[62],"integrals":[64],"involved":[65],"are":[66,79],"approximated":[67],"using":[68],"Chebyshev":[70],"interpolation":[71],"appropriate":[74],"Sinc":[75],"quadrature.":[76],"Numerical":[77],"examples":[78],"given":[80],"which":[81],"confirm":[82],"theoretical":[83],"results.":[84]},"counts_by_year":[{"year":2017,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}