{"id":"https://openalex.org/W4392972571","doi":"https://doi.org/10.1080/00207160.2024.2331700","title":"Euler wavelets operational matrix of integration and its\u00a0application in the calculus of variations","display_name":"Euler wavelets operational matrix of integration and its\u00a0application in the calculus of variations","publication_year":2024,"publication_date":"2024-03-20","ids":{"openalex":"https://openalex.org/W4392972571","doi":"https://doi.org/10.1080/00207160.2024.2331700"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2024.2331700","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2331700","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101969512","display_name":"Yanxin Wang","orcid":"https://orcid.org/0000-0001-9358-927X"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanxin Wang","raw_affiliation_strings":["Ningbo University of Technology","School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"Ningbo University of Technology","institution_ids":["https://openalex.org/I159389169"]},{"raw_affiliation_string":"School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083857790","display_name":"Li Zhu","orcid":"https://orcid.org/0000-0002-9805-6779"},"institutions":[{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Li Zhu","raw_affiliation_strings":["Ningbo University of Technology","School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"Ningbo University of Technology","institution_ids":["https://openalex.org/I159389169"]},{"raw_affiliation_string":"School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5113326348","display_name":"Dielan Hu","orcid":null},"institutions":[{"id":"https://openalex.org/I109935558","display_name":"Ningbo University","ror":"https://ror.org/03et85d35","country_code":"CN","type":"education","lineage":["https://openalex.org/I109935558"]},{"id":"https://openalex.org/I159389169","display_name":"Ningbo University of Technology","ror":"https://ror.org/037dym702","country_code":"CN","type":"education","lineage":["https://openalex.org/I159389169"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dielan Hu","raw_affiliation_strings":["Ningbo University","Ningbo University of Technology","School of Mathematics and Statistics, Ningbo University, Ningbo, China","School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China"],"affiliations":[{"raw_affiliation_string":"Ningbo University","institution_ids":["https://openalex.org/I109935558"]},{"raw_affiliation_string":"Ningbo University of Technology","institution_ids":["https://openalex.org/I159389169"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Ningbo University, Ningbo, China","institution_ids":["https://openalex.org/I109935558"]},{"raw_affiliation_string":"School of Statistics and Data Science, Ningbo University of Technology, Ningbo, China","institution_ids":["https://openalex.org/I159389169"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5083857790"],"corresponding_institution_ids":["https://openalex.org/I159389169"],"apc_list":null,"apc_paid":null,"fwci":0.8588,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.65480056,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"101","issue":"4","first_page":"386","last_page":"406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T13261","display_name":"Elasticity and Wave Propagation","score":0.9958000183105469,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T13487","display_name":"Statistical and numerical algorithms","score":0.9800000190734863,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.7169091105461121},{"id":"https://openalex.org/keywords/operational-calculus","display_name":"Operational calculus","score":0.6246904730796814},{"id":"https://openalex.org/keywords/matrix-calculus","display_name":"Matrix calculus","score":0.6175525188446045},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.5600205063819885},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.5283939242362976},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.5010414123535156},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4833661913871765},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4829265773296356},{"id":"https://openalex.org/keywords/semi-implicit-euler-method","display_name":"Semi-implicit Euler method","score":0.4821838438510895},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4254716634750366},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34296342730522156},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.31073155999183655},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.28663432598114014},{"id":"https://openalex.org/keywords/euler-equations","display_name":"Euler equations","score":0.22040978074073792},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1709204614162445}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7169091105461121},{"id":"https://openalex.org/C2779991855","wikidata":"https://www.wikidata.org/wiki/Q1162633","display_name":"Operational calculus","level":2,"score":0.6246904730796814},{"id":"https://openalex.org/C123282570","wikidata":"https://www.wikidata.org/wiki/Q29167","display_name":"Matrix calculus","level":3,"score":0.6175525188446045},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.5600205063819885},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.5283939242362976},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.5010414123535156},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4833661913871765},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4829265773296356},{"id":"https://openalex.org/C93082080","wikidata":"https://www.wikidata.org/wiki/Q5475314","display_name":"Semi-implicit Euler method","level":4,"score":0.4821838438510895},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4254716634750366},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34296342730522156},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.31073155999183655},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.28663432598114014},{"id":"https://openalex.org/C38409319","wikidata":"https://www.wikidata.org/wiki/Q375175","display_name":"Euler equations","level":2,"score":0.22040978074073792},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1709204614162445},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C39482219","wikidata":"https://www.wikidata.org/wiki/Q192826","display_name":"Kronecker delta","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2024.2331700","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2331700","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W779616253","https://openalex.org/W1971409566","https://openalex.org/W1975766919","https://openalex.org/W2002324029","https://openalex.org/W2015854079","https://openalex.org/W2023552712","https://openalex.org/W2025349820","https://openalex.org/W2030367564","https://openalex.org/W2033317678","https://openalex.org/W2033998066","https://openalex.org/W2078433315","https://openalex.org/W2085483400","https://openalex.org/W2094012975","https://openalex.org/W2144817836","https://openalex.org/W2409584460","https://openalex.org/W2583074839","https://openalex.org/W2896087590","https://openalex.org/W2914198344","https://openalex.org/W3097055902","https://openalex.org/W3109786339","https://openalex.org/W3134387060","https://openalex.org/W3186457152","https://openalex.org/W3204790508"],"related_works":["https://openalex.org/W2466040413","https://openalex.org/W2349703342","https://openalex.org/W4382053489","https://openalex.org/W2089955609","https://openalex.org/W92860307","https://openalex.org/W4320930571","https://openalex.org/W2753480721","https://openalex.org/W2606829290","https://openalex.org/W1178790052","https://openalex.org/W1674877062"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"Euler":[4,22,29,55],"wavelets":[5,23,30,56],"method":[6,57],"for":[7],"solving":[8],"the":[9,32,35,41,47,54,66,71],"variational":[10,36],"problems":[11,37],"is":[12],"presented.":[13],"The":[14],"operational":[15,33],"matrices":[16],"of":[17,21,43,53,70],"integration":[18],"and":[19,31,50,68],"product":[20],"are":[24,38,58,62],"calculated.":[25],"Then,":[26],"by":[27],"using":[28],"matrices,":[34],"reduced":[39],"into":[40],"system":[42],"algebraic":[44],"equations.":[45],"Furthermore,":[46],"convergence":[48],"analysis":[49],"error":[51],"bound":[52],"given.":[59],"Some":[60],"examples":[61],"included":[63],"to":[64],"demonstrate":[65],"applicability":[67],"validity":[69],"schemes.":[72]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}