{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T05:04:43Z","timestamp":1783746283115,"version":"3.55.0"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,12,30]],"date-time":"2024-12-30T00:00:00Z","timestamp":1735516800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Ministry of Science, Technological Development, and Innovation of the Republic of Serbia."}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this study, we discuss the symmetries underlying Bernstein polynomial differentiation matrices, as they are used in the collocation method approach to approximate solutions of initial and boundary value problems. The symmetries are brought into connection with those of the Chebyshev pseudospectral method (Chebyshev polynomial differentiation matrices). The treatment discussed here enables a faster and more accurate generation of differentiation matrices. The results are applied in numerical solutions of several initial value problems for the partial differential equation of convection\u2013diffusion reaction type. The method described herein demonstrates the combination of advanced numerical techniques like polynomial interpolation, stability-preserving timestepping, and transformation methods to solve a challenging nonlinear PDE efficiently. The use of Bernstein polynomials offers a high degree of accuracy for spatial discretization, and the CGL nodes improve the stability of the polynomial approximation. This analysis shows that exploiting symmetry in the differentiation matrices, combined with the wise choice of collocation nodes (CGL), leads to both accurate and efficient numerical methods for solving PDEs and accuracy that approach pseudospectral methods that use well-known orthogonal polynomials such as Chebyshev polynomials.<\/jats:p>","DOI":"10.3390\/sym17010047","type":"journal-article","created":{"date-parts":[[2024,12,31]],"date-time":"2024-12-31T14:21:12Z","timestamp":1735654872000},"page":"47","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Symmetries of Bernstein Polynomial Differentiation Matrices and Applications to Initial Value Problems"],"prefix":"10.3390","volume":"17","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3057-9784","authenticated-orcid":false,"given":"Nikola","family":"Mirkov","sequence":"first","affiliation":[{"name":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1645-2071","authenticated-orcid":false,"given":"Nicola","family":"Fabiano","sequence":"additional","affiliation":[{"name":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8885-2683","authenticated-orcid":false,"given":"Du\u0161an","family":"Nikezi\u0107","sequence":"additional","affiliation":[{"name":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4244-4342","authenticated-orcid":false,"given":"Vuk","family":"Stojiljkovi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Science, University of Novi Sad, Trg Dositeja Obradovi\u0107a 3, 21000 Novi Sad, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4546-782X","authenticated-orcid":false,"given":"Milica","family":"Ili\u0107","sequence":"additional","affiliation":[{"name":"\u2018Vin\u010da\u2019 Institute of Nuclear Sciences, National Institute of the Republic of Serbia, University of Belgrade, Mike Petrovi\u0107a Alasa 12-14, 11351 Belgrade, Serbia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Canuto, C., Hussaini, M.Y., Quarteroni, A., and Zang, T.A. 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