{"id":"https://openalex.org/W3137237050","doi":"https://doi.org/10.3390/sym13040536","title":"A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems","display_name":"A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems","publication_year":2021,"publication_date":"2021-03-25","ids":{"openalex":"https://openalex.org/W3137237050","doi":"https://doi.org/10.3390/sym13040536","mag":"3137237050"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040536","pdf_url":"https://www.mdpi.com/2073-8994/13/4/536/pdf?version=1616665411","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/536/pdf?version=1616665411","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5073337370","display_name":"Sharanjeet Dhawan","orcid":"https://orcid.org/0000-0003-2970-0169"},"institutions":[{"id":"https://openalex.org/I4210133503","display_name":"Central University of Haryana","ror":"https://ror.org/03mtwkv54","country_code":"IN","type":"education","lineage":["https://openalex.org/I4210133503"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Sharanjeet Dhawan","raw_affiliation_strings":["Department of Mathematics, Central University of Haryana, Haryana 123029, India"],"raw_orcid":"https://orcid.org/0000-0003-2970-0169","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Central University of Haryana, Haryana 123029, India","institution_ids":["https://openalex.org/I4210133503"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035539918","display_name":"J. A. Tenreiro Machado","orcid":"https://orcid.org/0000-0003-4274-4879"},"institutions":[{"id":"https://openalex.org/I83863532","display_name":"Polytechnic Institute of Porto","ror":"https://ror.org/04988re48","country_code":"PT","type":"education","lineage":["https://openalex.org/I83863532"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Jos\u00e9 A. Tenreir Machado","raw_affiliation_strings":["Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"],"raw_orcid":"https://orcid.org/0000-0003-4274-4879","affiliations":[{"raw_affiliation_string":"Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal","institution_ids":["https://openalex.org/I83863532"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051992194","display_name":"Dariusz W. Brzezi\u0144ski","orcid":"https://orcid.org/0000-0001-7207-5253"},"institutions":[{"id":"https://openalex.org/I188884621","display_name":"Lodz University of Technology","ror":"https://ror.org/00s8fpf52","country_code":"PL","type":"education","lineage":["https://openalex.org/I188884621"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Dariusz W. Brzezi\u0144ski","raw_affiliation_strings":["Institute of Applied Computer Science, Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 \u0141\u00f3d\u017a, Poland"],"raw_orcid":"https://orcid.org/0000-0001-7207-5253","affiliations":[{"raw_affiliation_string":"Institute of Applied Computer Science, Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology, ul. Stefanowskiego 18/22, 90-924 \u0141\u00f3d\u017a, Poland","institution_ids":["https://openalex.org/I188884621"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041689394","display_name":"M.S. Osman","orcid":"https://orcid.org/0000-0002-5783-0940"},"institutions":[{"id":"https://openalex.org/I145487455","display_name":"Cairo University","ror":"https://ror.org/03q21mh05","country_code":"EG","type":"education","lineage":["https://openalex.org/I145487455"]},{"id":"https://openalex.org/I199693650","display_name":"Umm al-Qura University","ror":"https://ror.org/01xjqrm90","country_code":"SA","type":"education","lineage":["https://openalex.org/I199693650"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Mohamed S. Osman","raw_affiliation_strings":["Department of Mathematics, Faculty of Applied Science, Umm Alqurah University, Makkah 21955, Saudi Arabia","Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt"],"raw_orcid":"https://orcid.org/0000-0002-5783-0940","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Applied Science, Umm Alqurah University, Makkah 21955, Saudi Arabia","institution_ids":["https://openalex.org/I199693650"]},{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt","institution_ids":["https://openalex.org/I145487455"]}]}],"institutions":[],"countries_distinct_count":5,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5041689394"],"corresponding_institution_ids":["https://openalex.org/I145487455","https://openalex.org/I199693650"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":2.2805,"has_fulltext":false,"cited_by_count":27,"citation_normalized_percentile":{"value":0.882991,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"13","issue":"4","first_page":"536","last_page":"536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958999752998352,"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"}},"topics":[{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9925000071525574,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9805999994277954,"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/wavelet","display_name":"Wavelet","score":0.6904465556144714},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.653762698173523},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.631462037563324},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.6015812158584595},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5795904994010925},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.5606095194816589},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5501752495765686},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5467199683189392},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5385713577270508},{"id":"https://openalex.org/keywords/chebyshev-iteration","display_name":"Chebyshev iteration","score":0.5373514890670776},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4714394807815552},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.4530401825904846},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.4527084231376648},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.4509042799472809},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3995249271392822},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.38361650705337524},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25094401836395264},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2403813600540161},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.11565172672271729},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.07753270864486694},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06069192290306091}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6904465556144714},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.653762698173523},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.631462037563324},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.6015812158584595},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5795904994010925},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.5606095194816589},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5501752495765686},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5467199683189392},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5385713577270508},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.5373514890670776},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4714394807815552},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.4530401825904846},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.4527084231376648},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.4509042799472809},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3995249271392822},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.38361650705337524},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25094401836395264},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2403813600540161},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.11565172672271729},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.07753270864486694},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06069192290306091},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13040536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040536","pdf_url":"https://www.mdpi.com/2073-8994/13/4/536/pdf?version=1616665411","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:65d634d4bba541dd89d30f4f74633802","is_oa":true,"landing_page_url":"https://doaj.org/article/65d634d4bba541dd89d30f4f74633802","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 4, p 536 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/536/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040536","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry; Volume 13; Issue 4; Pages: 536","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13040536","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040536","pdf_url":"https://www.mdpi.com/2073-8994/13/4/536/pdf?version=1616665411","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3137237050.pdf"},"referenced_works_count":36,"referenced_works":["https://openalex.org/W1965266376","https://openalex.org/W1970547977","https://openalex.org/W1973769870","https://openalex.org/W2000924596","https://openalex.org/W2013363617","https://openalex.org/W2029289888","https://openalex.org/W2029911730","https://openalex.org/W2040573322","https://openalex.org/W2045434085","https://openalex.org/W2062024414","https://openalex.org/W2072499605","https://openalex.org/W2087482043","https://openalex.org/W2089281733","https://openalex.org/W2090303355","https://openalex.org/W2105505702","https://openalex.org/W2151871085","https://openalex.org/W2158721499","https://openalex.org/W2162667590","https://openalex.org/W2614366477","https://openalex.org/W2736655775","https://openalex.org/W2737076214","https://openalex.org/W2739112587","https://openalex.org/W2765313399","https://openalex.org/W2781754946","https://openalex.org/W2792027044","https://openalex.org/W2907755002","https://openalex.org/W2928571377","https://openalex.org/W2934529063","https://openalex.org/W2963238677","https://openalex.org/W2998441866","https://openalex.org/W3087352120","https://openalex.org/W3097761003","https://openalex.org/W4232769230","https://openalex.org/W4254246953","https://openalex.org/W4255272544","https://openalex.org/W6770226917"],"related_works":["https://openalex.org/W2112919228","https://openalex.org/W1585782015","https://openalex.org/W2136992695","https://openalex.org/W1512440940","https://openalex.org/W2021099221","https://openalex.org/W2054912819","https://openalex.org/W2588042187","https://openalex.org/W2979693432","https://openalex.org/W2135245226","https://openalex.org/W3048174355"],"abstract_inverted_index":{"In":[0],"the":[1,17,28,32,49,53,56,64,77,82],"past":[2],"decade,":[3],"various":[4],"types":[5],"of":[6,19,22,35,55,81],"wavelet-based":[7],"algorithms":[8],"were":[9],"proposed,":[10],"leading":[11],"to":[12],"a":[13,20],"key":[14],"tool":[15],"in":[16],"solution":[18,34],"number":[21],"numerical":[23,33],"problems.":[24],"This":[25],"work":[26],"adopts":[27],"Chebyshev":[29,39],"wavelets":[30],"for":[31,44,63,72],"several":[36,73],"models.":[37],"A":[38],"operational":[40],"matrix":[41],"is":[42],"developed,":[43],"selected":[45],"collocation":[46],"points,":[47],"using":[48],"fundamental":[50],"properties.":[51],"Moreover,":[52],"convergence":[54],"expansion":[57],"coefficients":[58],"and":[59,79],"an":[60],"upper":[61],"estimate":[62],"truncation":[65],"error":[66],"are":[67],"included.":[68],"The":[69],"obtained":[70],"results":[71],"case":[74],"studies":[75],"illustrate":[76],"accuracy":[78],"reliability":[80],"proposed":[83],"approach.":[84]},"counts_by_year":[{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":7},{"year":2022,"cited_by_count":10},{"year":2021,"cited_by_count":6}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2021-03-29T00:00:00"}
