{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T00:09:49Z","timestamp":1785370189336,"version":"3.55.0"},"reference-count":34,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T00:00:00Z","timestamp":1616630400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Institute of Applied Computer Science, Faculty of Electrical, Electronic, Computer and Control Engineering, Lodz University of Technology as a part of the statutory activity","award":["nr 501\/2-24-1-2"],"award-info":[{"award-number":["nr 501\/2-24-1-2"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In the past decade, various types of wavelet-based algorithms were proposed, leading to a key tool in the solution of a number of numerical problems. This work adopts the Chebyshev wavelets for the numerical solution of several models. A Chebyshev operational matrix is developed, for selected collocation points, using the fundamental properties. Moreover, the convergence of the expansion coefficients and an upper estimate for the truncation error are included. The obtained results for several case studies illustrate the accuracy and reliability of the proposed approach.<\/jats:p>","DOI":"10.3390\/sym13040536","type":"journal-article","created":{"date-parts":[[2021,3,25]],"date-time":"2021-03-25T21:09:45Z","timestamp":1616706585000},"page":"536","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":26,"title":["A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2970-0169","authenticated-orcid":false,"given":"Sharanjeet","family":"Dhawan","sequence":"first","affiliation":[{"name":"Department of Mathematics, Central University of Haryana, Haryana 123029, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"Jos\u00e9 A. Tenreir","family":"Machado","sequence":"additional","affiliation":[{"name":"Institute of Engineering, Polytechnic of Porto, Department of Electrical Engineering, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4249-015 Porto, Portugal"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7207-5253","authenticated-orcid":false,"given":"Dariusz W.","family":"Brzezi\u0144ski","sequence":"additional","affiliation":[{"name":"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"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5783-0940","authenticated-orcid":false,"given":"Mohamed S.","family":"Osman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Cairo University, Giza 12613, Egypt"},{"name":"Department of Mathematics, Faculty of Applied Science, Umm Alqurah University, Makkah 21955, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,3,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1554","DOI":"10.1007\/s10915-017-0506-8","article-title":"Spectral Methods for Substantial Fractional Differential Equations","volume":"74","author":"Huang","year":"2018","journal-title":"J. Sci. 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