{"id":"https://openalex.org/W1980202545","doi":"https://doi.org/10.2478/cmam-2009-0004","title":"A Metod with a Controllable Exponential Convergence Rate for Nonlinear Differential Operator Equations","display_name":"A Metod with a Controllable Exponential Convergence Rate for Nonlinear Differential Operator Equations","publication_year":2009,"publication_date":"2009-01-01","ids":{"openalex":"https://openalex.org/W1980202545","doi":"https://doi.org/10.2478/cmam-2009-0004","mag":"1980202545"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2009-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0004","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0004/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5055970222","display_name":"I.P. Gavrilyuk","orcid":null},"institutions":[{"id":"https://openalex.org/I4210106901","display_name":"International University of Cooperative Education","ror":"https://ror.org/01nbps758","country_code":"DE","type":"education","lineage":["https://openalex.org/I4210106901"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"I.P. Gavrilyuk","raw_affiliation_strings":["1University of Cooperative Education, Berufsakademie Eisenach, Staatliche Studienakademie Th\u00a8uringen, Am Wartenberg 2, D-99817 Eisenach, Germany"],"affiliations":[{"raw_affiliation_string":"1University of Cooperative Education, Berufsakademie Eisenach, Staatliche Studienakademie Th\u00a8uringen, Am Wartenberg 2, D-99817 Eisenach, Germany","institution_ids":["https://openalex.org/I4210106901"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074960233","display_name":"I. I. Lazurchak","orcid":null},"institutions":[{"id":"https://openalex.org/I41545563","display_name":"Presbyterian University, Ghana","ror":"https://ror.org/02369cb65","country_code":"GH","type":"education","lineage":["https://openalex.org/I41545563"]}],"countries":["GH"],"is_corresponding":false,"raw_author_name":"I. I. Lazurchak","raw_affiliation_strings":["2Drogobych State Pedagogical University, I. Franka str., 34, Drogobych, Ukraine"],"affiliations":[{"raw_affiliation_string":"2Drogobych State Pedagogical University, I. Franka str., 34, Drogobych, Ukraine","institution_ids":["https://openalex.org/I41545563"]}]},{"author_position":"middle","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/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":"V. L. Makarov","raw_affiliation_strings":["3Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs\u2019ka str., Kyiv-4, 01601, Ukraine"],"affiliations":[{"raw_affiliation_string":"3Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs\u2019ka str., Kyiv-4, 01601, Ukraine","institution_ids":["https://openalex.org/I190444043"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5090808357","display_name":"Dmytro Sytnyk","orcid":"https://orcid.org/0000-0003-3065-4921"},"institutions":[{"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":"D. Sytnyk","raw_affiliation_strings":["3Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs\u2019ka str., Kyiv-4, 01601, Ukraine"],"affiliations":[{"raw_affiliation_string":"3Institute of Mathematics of NAS of Ukraine, 3 Tereshchenkivs\u2019ka str., Kyiv-4, 01601, Ukraine","institution_ids":["https://openalex.org/I190444043"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5055970222"],"corresponding_institution_ids":["https://openalex.org/I4210106901"],"apc_list":null,"apc_paid":null,"fwci":0.3534,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.59629715,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"9","issue":"1","first_page":"63","last_page":"78"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9842000007629395,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9842000007629395,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9829999804496765,"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":0.982200026512146,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.7155705690383911},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6805921792984009},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6492650508880615},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.6453997492790222},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6353331208229065},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5688132643699646},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.478670209646225},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4715335965156555},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47063255310058594},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14854657649993896},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07138699293136597},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.05904480814933777}],"concepts":[{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.7155705690383911},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6805921792984009},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6492650508880615},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.6453997492790222},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6353331208229065},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5688132643699646},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.478670209646225},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4715335965156555},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47063255310058594},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14854657649993896},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07138699293136597},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.05904480814933777},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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:10.2478/cmam-2009-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0004","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.2478/cmam-2009-0004","is_oa":true,"landing_page_url":"https://doi.org/10.2478/cmam-2009-0004","pdf_url":"https://www.degruyter.com/document/doi/10.2478/cmam-2009-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"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/W1980202545.pdf","grobid_xml":"https://content.openalex.org/works/W1980202545.grobid-xml"},"referenced_works_count":23,"referenced_works":["https://openalex.org/W1542744440","https://openalex.org/W1560556759","https://openalex.org/W1965088360","https://openalex.org/W1969682207","https://openalex.org/W1982929501","https://openalex.org/W1997290136","https://openalex.org/W2000062047","https://openalex.org/W2003306789","https://openalex.org/W2006367435","https://openalex.org/W2017739665","https://openalex.org/W2031567600","https://openalex.org/W2084111268","https://openalex.org/W2108329179","https://openalex.org/W2136404093","https://openalex.org/W2151748147","https://openalex.org/W2485016249","https://openalex.org/W2577663557","https://openalex.org/W4205604664","https://openalex.org/W4242212920","https://openalex.org/W4254708785","https://openalex.org/W4292170110","https://openalex.org/W4302769929","https://openalex.org/W6629280276"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2281834912","https://openalex.org/W1489941249","https://openalex.org/W3123492739","https://openalex.org/W4320486059","https://openalex.org/W2494168571","https://openalex.org/W3121191496","https://openalex.org/W1550676882","https://openalex.org/W1992626918","https://openalex.org/W2033096984"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"propose":[2],"a":[3],"new":[4],"analytical-numerical":[5],"method":[6,20],"with":[7],"an":[8],"embedded":[9],"convergence":[10,24],"control":[11],"mechanism":[12],"for":[13],"solving":[14],"nonlinear":[15],"operator":[16],"differential":[17],"equations.":[18],"The":[19],"provides":[21],"the":[22,30],"exponential":[23],"rate.":[25],"A":[26],"numerical":[27],"example":[28],"confirms":[29],"theoretical":[31],"results.":[32]},"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}