{"id":"https://openalex.org/W4416343247","doi":"https://doi.org/10.48550/arxiv.2511.11082","title":"Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials","display_name":"Numerical approximation of Caputo-type advection-diffusion equations in one and multiple spatial dimensions via shifted Chebyshev polynomials","publication_year":2025,"publication_date":"2025-11-14","ids":{"openalex":"https://openalex.org/W4416343247","doi":"https://doi.org/10.48550/arxiv.2511.11082"},"language":null,"primary_location":{"id":"pmh:oai:arXiv.org:2511.11082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.11082","pdf_url":"https://arxiv.org/pdf/2511.11082","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2511.11082","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"de la Hoz, Francisco","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de la Hoz, Francisco","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030335412","display_name":"Peru Muniain","orcid":"https://orcid.org/0000-0002-7796-0304"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muniain, Peru","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9146999716758728,"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":0.9146999716758728,"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/T12303","display_name":"Tensor decomposition and applications","score":0.04399999976158142,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.007600000128149986,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.7919999957084656},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6657999753952026},{"id":"https://openalex.org/keywords/chebyshev-pseudospectral-method","display_name":"Chebyshev pseudospectral method","score":0.5508000254631042},{"id":"https://openalex.org/keywords/chebyshev-equation","display_name":"Chebyshev equation","score":0.5501999855041504},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.5113000273704529},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.5048999786376953},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.49129998683929443},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.46790000796318054}],"concepts":[{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.7919999957084656},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.760699987411499},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6657999753952026},{"id":"https://openalex.org/C122107654","wikidata":"https://www.wikidata.org/wiki/Q5089017","display_name":"Chebyshev pseudospectral method","level":5,"score":0.5508000254631042},{"id":"https://openalex.org/C142484921","wikidata":"https://www.wikidata.org/wiki/Q3890369","display_name":"Chebyshev equation","level":4,"score":0.5501999855041504},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.5113000273704529},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5105999708175659},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.5048999786376953},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.49129998683929443},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.46790000796318054},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45590001344680786},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.40070000290870667},{"id":"https://openalex.org/C2780365114","wikidata":"https://www.wikidata.org/wiki/Q169478","display_name":"MATLAB","level":2,"score":0.3937000036239624},{"id":"https://openalex.org/C196512905","wikidata":"https://www.wikidata.org/wiki/Q2457511","display_name":"Chebyshev iteration","level":3,"score":0.382999986410141},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.37540000677108765},{"id":"https://openalex.org/C9353750","wikidata":"https://www.wikidata.org/wiki/Q5384549","display_name":"Equioscillation theorem","level":5,"score":0.37470000982284546},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.3709999918937683},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.32109999656677246},{"id":"https://openalex.org/C2986878899","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical approximation","level":3,"score":0.3172999918460846},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.26330000162124634},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C20160815","wikidata":"https://www.wikidata.org/wiki/Q1482452","display_name":"Sylvester matrix","level":5,"score":0.2538999915122986}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.11082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.11082","pdf_url":"https://arxiv.org/pdf/2511.11082","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2511.11082","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.11082","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2511.11082","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.11082","pdf_url":"https://arxiv.org/pdf/2511.11082","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"In":[0,27],"this":[1,98],"paper,":[2],"using":[3],"a":[4,71],"pseudospectral":[5],"approach,":[6],"we":[7,37,43],"develop":[8],"operational":[9],"matrices":[10,35,48],"based":[11],"on":[12],"the":[13,31,45,64,67,95],"shifted":[14],"Chebyshev":[15],"polynomials":[16],"to":[17,29,49],"approximate":[18],"numerically":[19,51],"Caputo":[20,46],"fractional":[21,25],"derivatives":[22],"and":[23,57],"Riemann-Liouville":[24],"integrals.":[26],"order":[28],"make":[30],"generation":[32],"of":[33,66,97],"these":[34],"stable,":[36],"use":[38],"variable":[39],"precision":[40],"arithmetic.":[41],"Then,":[42],"apply":[44],"differentiation":[47],"solve":[50],"Caputo-type":[52],"advection-diffusion":[53],"equations":[54],"in":[55,92],"one":[56],"multiple":[58],"spatial":[59],"dimensions,":[60],"which":[61],"involves":[62],"transforming":[63],"discretization":[65],"concerning":[68],"equation":[69],"into":[70],"Sylvester":[72],"(tensor)":[73],"equation.":[74],"We":[75],"provide":[76],"complete":[77],"Matlab":[78],"codes,":[79],"whose":[80],"implementation":[81],"is":[82],"carefully":[83],"explained.":[84],"The":[85],"numerical":[86],"experiments":[87],"involving":[88],"highly":[89],"oscillatory":[90],"functions":[91],"time":[93],"confirm":[94],"effectiveness":[96],"approach.":[99]},"counts_by_year":[],"updated_date":"2026-07-03T08:13:44.112507","created_date":"2025-11-18T00:00:00"}
