{"id":"https://openalex.org/W2090581346","doi":"https://doi.org/10.1090/s0025-5718-04-01720-x","title":"Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces","display_name":"Algorithms without accuracy saturation for evolution equations in Hilbert and Banach spaces","publication_year":2004,"publication_date":"2004-10-27","ids":{"openalex":"https://openalex.org/W2090581346","doi":"https://doi.org/10.1090/s0025-5718-04-01720-x","mag":"2090581346"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-04-01720-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01720-x","pdf_url":"https://www.ams.org/mcom/2005-74-250/S0025-5718-04-01720-X/S0025-5718-04-01720-X.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/2005-74-250/S0025-5718-04-01720-X/S0025-5718-04-01720-X.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":["Berufsakademie Th\u00c3\u00bcringen, Am Wartenberg 2, D-99817 Eisenach, Germany","Berufsakademie Th\u00fcringen, Am Wartenberg 2, D-99817 Eisenach, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Berufsakademie Th\u00c3\u00bcringen, Am Wartenberg 2, D-99817 Eisenach, Germany","institution_ids":[]},{"raw_affiliation_string":"Berufsakademie Th\u00fcringen, 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, Tereschen- kivska 3, 01601 Kiev, Ukraine"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Academy of Sciences of Ukraine, Institute of Mathematics, Tereschen- kivska 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":3.3939,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.92069393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"74","issue":"250","first_page":"555","last_page":"583"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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":0.9983999729156494,"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/T11416","display_name":"Numerical methods for differential equations","score":0.998199999332428,"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/mathematics","display_name":"Mathematics","score":0.9132013320922852},{"id":"https://openalex.org/keywords/banach-space","display_name":"Banach space","score":0.6486619710922241},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.6047137975692749},{"id":"https://openalex.org/keywords/saturation","display_name":"Saturation (graph theory)","score":0.5108744502067566},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.44827014207839966},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.43002066016197205},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.4091915488243103},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11096692085266113}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9132013320922852},{"id":"https://openalex.org/C132954091","wikidata":"https://www.wikidata.org/wiki/Q194397","display_name":"Banach space","level":2,"score":0.6486619710922241},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.6047137975692749},{"id":"https://openalex.org/C9930424","wikidata":"https://www.wikidata.org/wiki/Q7426587","display_name":"Saturation (graph theory)","level":2,"score":0.5108744502067566},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.44827014207839966},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43002066016197205},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.4091915488243103},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11096692085266113}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-04-01720-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01720-x","pdf_url":"https://www.ams.org/mcom/2005-74-250/S0025-5718-04-01720-X/S0025-5718-04-01720-X.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.152.9962","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.152.9962","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/2005-74-250/S0025-5718-04-01720-X/S0025-5718-04-01720-X.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-04-01720-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-04-01720-x","pdf_url":"https://www.ams.org/mcom/2005-74-250/S0025-5718-04-01720-X/S0025-5718-04-01720-X.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":null,"license_id":null,"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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2090581346.pdf","grobid_xml":"https://content.openalex.org/works/W2090581346.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W72179873","https://openalex.org/W563024366","https://openalex.org/W599293027","https://openalex.org/W621351040","https://openalex.org/W1516587486","https://openalex.org/W1527296550","https://openalex.org/W1569304948","https://openalex.org/W1972210335","https://openalex.org/W1994466299","https://openalex.org/W1995356931","https://openalex.org/W1998665522","https://openalex.org/W2012405708","https://openalex.org/W2018419001","https://openalex.org/W2030565709","https://openalex.org/W2031667286","https://openalex.org/W2035766380","https://openalex.org/W2043432681","https://openalex.org/W2055175862","https://openalex.org/W2060176450","https://openalex.org/W2408478130","https://openalex.org/W3038165843","https://openalex.org/W3042562017","https://openalex.org/W3135434763","https://openalex.org/W4240555338","https://openalex.org/W4242517046","https://openalex.org/W4246792763","https://openalex.org/W4293185733","https://openalex.org/W4298060601","https://openalex.org/W4300794954"],"related_works":["https://openalex.org/W2037791951","https://openalex.org/W1507633639","https://openalex.org/W1721151596","https://openalex.org/W2023502046","https://openalex.org/W310085760","https://openalex.org/W3108554747","https://openalex.org/W2442302306","https://openalex.org/W2019092692","https://openalex.org/W2778854810","https://openalex.org/W2366242676"],"abstract_inverted_index":{"We":[0,63],"consider":[1],"the":[2,6,9,48,76,81,84,89,107,139,198,202,210],"Cauchy":[3],"problem":[4],"for":[5],"first":[7],"and":[8,16,71,137,195],"second":[10],"order":[11],"differential":[12],"equations":[13],"in":[14],"Banach":[15],"Hilbert":[17],"spaces":[18],"with":[19,67,175],"an":[20],"operator":[21,108,140,178],"coefficient":[22],"<inline-formula":[23,50,110,143,179],"content-type=\"math/mathml\">":[24,51,111,144,180],"<mml:math":[25,52,112,145,181],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[26,53,113,146,182],"alttext=\"upper":[27,183],"A":[28,150],"left-parenthesis":[29],"t":[30,117],"right-parenthesis\">":[31],"<mml:semantics>":[32,55,120,153,185],"<mml:mrow>":[33,154],"<mml:mi>A</mml:mi>":[34,129,162,186],"<mml:mo":[35,38],"stretchy=\"false\">(</mml:mo>":[36],"<mml:mi>t</mml:mi>":[37,56,128,164],"stretchy=\"false\">)</mml:mo>":[39],"</mml:mrow>":[40,130,165,166],"<mml:annotation":[41,57,132,167,187],"encoding=\"application/x-tex\">A(t)</mml:annotation>":[42],"</mml:semantics>":[43,59,134,172,189],"</mml:math>":[44,60,135,173,190],"</inline-formula>":[45,61,136,174,191],"depending":[46],"on":[47,197],"parameter":[49],"alttext=\"t\">":[54],"encoding=\"application/x-tex\">t</mml:annotation>":[58],".":[62],"develop":[64],"discretization":[65],"methods":[66],"high":[68],"parallelism":[69],"level":[70],"without":[72],"accuracy":[73,77,194],"saturation;":[74],"i.e.,":[75],"adapts":[78],"automatically":[79],"to":[80],"smoothness":[82],"of":[83,91,103,106,138,201,207],"solution.":[85],"For":[86],"analytical":[87],"solutions":[88,208],"rate":[90],"convergence":[92],"is":[93],"exponential.":[94],"These":[95],"results":[96],"can":[97],"be":[98],"viewed":[99],"as":[100],"a":[101,176],"development":[102],"parallel":[104],"approximations":[105,200],"exponential":[109,193],"alttext=\"e":[114],"Superscript":[115],"minus":[116],"upper":[118,149],"A\">":[119,184],"<mml:msup>":[121],"<mml:mi>e</mml:mi>":[122],"<mml:mrow":[123,159],"class=\"MJX-TeXAtom-ORD\">":[124,160],"<mml:mo>":[125,156],"\u2212":[126],"</mml:mo>":[127,158],"</mml:msup>":[131],"encoding=\"application/x-tex\">e^{-tA}</mml:annotation>":[133],"cosine":[141],"family":[142],"alttext=\"cosine":[147],"StartRoot":[148],"EndRoot":[151],"t\">":[152],"<mml:mi>cos</mml:mi>":[155],"\u2061":[157],"<mml:msqrt>":[161],"</mml:msqrt>":[163],"encoding=\"application/x-tex\">\\cos":[168],"{\\sqrt":[169],"{A}":[170],"t}</mml:annotation>":[171],"constant":[177],"encoding=\"application/x-tex\">A</mml:annotation>":[188],"possessing":[192],"based":[196],"Sinc-quadrature":[199],"corresponding":[203],"Dunford-Cauchy":[204],"integral":[205],"representations":[206],"or":[209],"solution":[211],"operators.":[212]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
