{"id":"https://openalex.org/W4409342395","doi":"https://doi.org/10.1007/s10915-025-02880-7","title":"Taylor\u2013Fourier Approximation","display_name":"Taylor\u2013Fourier Approximation","publication_year":2025,"publication_date":"2025-04-10","ids":{"openalex":"https://openalex.org/W4409342395","doi":"https://doi.org/10.1007/s10915-025-02880-7"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-02880-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-02880-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/s10915-025-02880-7","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080721929","display_name":"M. P. Calvo","orcid":null},"institutions":[{"id":"https://openalex.org/I108103353","display_name":"Universidad de Valladolid","ror":"https://ror.org/01fvbaw18","country_code":"ES","type":"education","lineage":["https://openalex.org/I108103353"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"M. P. Calvo","raw_affiliation_strings":["IMUVA and Departamento de Matem\u00e1tica Aplicada, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain"],"affiliations":[{"raw_affiliation_string":"IMUVA and Departamento de Matem\u00e1tica Aplicada, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain","institution_ids":["https://openalex.org/I108103353"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005856573","display_name":"Joseba Makazaga","orcid":"https://orcid.org/0000-0002-7453-4844"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"J. Makazaga","raw_affiliation_strings":["Dpto. KZAA/CCIA, Facultad de Inform\u00e1tica, Universidad del Pais Vasco (UPV/EHU), Donostia-San Sebasti\u00e1n, Spain"],"affiliations":[{"raw_affiliation_string":"Dpto. KZAA/CCIA, Facultad de Inform\u00e1tica, Universidad del Pais Vasco (UPV/EHU), Donostia-San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5099054937","display_name":"A. Murua","orcid":null},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"A. Murua","raw_affiliation_strings":["Dpto. KZAA/CCIA, Facultad de Inform\u00e1tica, Universidad del Pais Vasco (UPV/EHU), Donostia-San Sebasti\u00e1n, Spain"],"affiliations":[{"raw_affiliation_string":"Dpto. KZAA/CCIA, Facultad de Inform\u00e1tica, Universidad del Pais Vasco (UPV/EHU), Donostia-San Sebasti\u00e1n, Spain","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5080721929"],"corresponding_institution_ids":["https://openalex.org/I108103353"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.09485328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"103","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9997000098228455,"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":0.9994000196456909,"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/mathematics","display_name":"Mathematics","score":0.8091399669647217},{"id":"https://openalex.org/keywords/fourier-series","display_name":"Fourier series","score":0.522704005241394},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5197636485099792},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.4844053387641907},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4456855058670044}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8091399669647217},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.522704005241394},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5197636485099792},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.4844053387641907},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4456855058670044}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-02880-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-02880-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1007/s10915-025-02880-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-025-02880-7","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1551845173","display_name":null,"funder_award_id":"VA169P20","funder_id":"https://openalex.org/F4320328351","funder_display_name":"Junta de Castilla y Le\u00f3n"},{"id":"https://openalex.org/G2016026724","display_name":null,"funder_award_id":"ITI456-22","funder_id":"https://openalex.org/F4320316131","funder_display_name":"Hezkuntza, Hizkuntza Politika Eta Kultura Saila, Eusko Jaurlaritza"},{"id":"https://openalex.org/G5742873783","display_name":null,"funder_award_id":"PID2022-136585NB-C22","funder_id":"https://openalex.org/F4320335598","funder_display_name":"Agencia Estatal de Investigaci\u00f3n"}],"funders":[{"id":"https://openalex.org/F4320316131","display_name":"Hezkuntza, Hizkuntza Politika Eta Kultura Saila, Eusko Jaurlaritza","ror":null},{"id":"https://openalex.org/F4320328351","display_name":"Junta de Castilla y Le\u00f3n","ror":"https://ror.org/02s8dab97"},{"id":"https://openalex.org/F4320335598","display_name":"Agencia Estatal de Investigaci\u00f3n","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W34573016","https://openalex.org/W1490180844","https://openalex.org/W1493815990","https://openalex.org/W1966991416","https://openalex.org/W2004974504","https://openalex.org/W2005061077","https://openalex.org/W2011378962","https://openalex.org/W2111563694","https://openalex.org/W2119372460","https://openalex.org/W2120575449","https://openalex.org/W2144144709","https://openalex.org/W2318896519","https://openalex.org/W2618966431","https://openalex.org/W2619381903","https://openalex.org/W2737053717","https://openalex.org/W3191571649","https://openalex.org/W4211077197","https://openalex.org/W4242108514"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2094657987","https://openalex.org/W2122827492","https://openalex.org/W2320412982","https://openalex.org/W4387646299","https://openalex.org/W2125702822","https://openalex.org/W2034847025","https://openalex.org/W2114993544"],"abstract_inverted_index":{"Abstract":[0],"In":[1,169],"this":[2,214],"paper,":[3],"we":[4],"introduce":[5],"an":[6,23,219],"algorithm":[7],"that":[8,149,190,242],"provides":[9],"approximate":[10,57],"solutions":[11,58],"to":[12,217,252],"semi-linear":[13,183],"ordinary":[14],"differential":[15],"equations":[16,179],"with":[17,34,232,257],"highly":[18,196],"oscillatory":[19,197],"solutions,":[20],"which,":[21],"after":[22],"appropriate":[24],"change":[25],"of":[26,132,176,213,246],"variables,":[27],"can":[28],"be":[29],"rewritten":[30],"as":[31,64,155,185,187],"non-autonomous":[32],"systems":[33],"a":[35,97,113,262],"$$(2\\pi":[36],"/\\omega":[37],")$$":[38],"<mml:math":[39,68,84,104,123,143,160,205],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[40,69,85,105,124,144,161,206],"<mml:mrow>":[41,70,86,162],"<mml:mo>(</mml:mo>":[42,72,88],"<mml:mn>2</mml:mn>":[43],"<mml:mi>\u03c0</mml:mi>":[44],"<mml:mo>/</mml:mo>":[45],"<mml:mi>\u03c9</mml:mi>":[46,73,145,163,207],"<mml:mo>)</mml:mo>":[47,77,92],"</mml:mrow>":[48,78,93,166],"</mml:math>":[49,79,94,107,126,146,167,208],"-periodic":[50],"dependence":[51],"on":[52],"t":[53,110,118],".":[54,168],"The":[55,210],"proposed":[56,248],"are":[59,137,191],"given":[60],"in":[61,101,117,140,194],"closed":[62],"form":[63],"functions":[65],"$$X(\\omega":[66],"t,t)$$":[67],"<mml:mi>X</mml:mi>":[71,87],"<mml:mi>t</mml:mi>":[74,76,91],"<mml:mo>,</mml:mo>":[75,90],",":[80,127,147],"where":[81],"$$X(\\theta":[82],",t)$$":[83],"<mml:mi>\u03b8</mml:mi>":[89,106,125],"is":[95,216],"(i)":[96],"truncated":[98,114,228],"Fourier":[99,235],"series":[100,116,230],"$$\\theta":[102,121],"$$":[103,122,142,159,204],"for":[108,119,180,200,222],"fixed":[109,120],"and":[111,261],"(ii)":[112],"Taylor":[115],"which":[128],"motivates":[129],"the":[130,133,174,181,195,233,244,247,253],"name":[131],"method.":[134],"These":[135],"approximations":[136,172,225],"uniformly":[138],"accurate":[139],"$$\\omega":[141,156,203],"meaning":[148],"their":[150],"accuracy":[151],"does":[152],"not":[153],"degrade":[154],"\\rightarrow":[157],"\\infty":[158],"<mml:mo>\u2192</mml:mo>":[164],"<mml:mi>\u221e</mml:mi>":[165],"addition,":[170],"Taylor\u2013Fourier":[171],"enable":[173],"computation":[175],"high-order":[177],"averaging":[178],"original":[182],"system,":[184],"well":[186],"related":[188],"maps":[189],"particularly":[192],"useful":[193],"regime":[198],"(i.e.,":[199],"sufficiently":[201],"large":[202],").":[209],"main":[211],"goal":[212],"paper":[215],"develop":[218],"efficient":[220],"procedure":[221],"computing":[223],"such":[224],"by":[226],"combining":[227],"power":[229],"arithmetic":[231],"Fast":[234],"Transform":[236],"(FFT).":[237],"We":[238],"present":[239],"numerical":[240],"experiments":[241],"illustrate":[243],"effectiveness":[245],"method,":[249],"including":[250],"applications":[251],"nonlinear":[254],"Schr\u00f6dinger":[255],"equation":[256],"non-smooth":[258],"initial":[259],"data":[260],"perturbed":[263],"Kepler":[264],"problem":[265],"from":[266],"satellite":[267],"orbit":[268],"dynamics.":[269]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}