A numerical approach for solving variable order differential equations using Bernstein polynomials
In this study, a numerical technique is applied to investigate solutions of linear variable order differential equations(VODEs) in fluid mechanics. We investigate variable order(VO) in the Caputo sense. Our aim is to apply Bernstein polynomials(Bps) as the basis functions and operational matrices. W...
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| Format: | Article |
| Language: | English |
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Elsevier
2020-10-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682030212X |
| _version_ | 1819068124516843520 |
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| author | Nematollah Kadkhoda |
| author_facet | Nematollah Kadkhoda |
| author_sort | Nematollah Kadkhoda |
| collection | DOAJ |
| description | In this study, a numerical technique is applied to investigate solutions of linear variable order differential equations(VODEs) in fluid mechanics. We investigate variable order(VO) in the Caputo sense. Our aim is to apply Bernstein polynomials(Bps) as the basis functions and operational matrices. We calculate two types of operational matrices of Bps. Using these operational matrices the main equation can be transformed into a system of algebraic equations, which must then be solved to get approximate solutions. Some examples are provided to indicate the accuracy of the presented method. |
| first_indexed | 2024-12-21T16:29:10Z |
| format | Article |
| id | doaj.art-df3578274bc645949712a3fecea6746c |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-12-21T16:29:10Z |
| publishDate | 2020-10-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-df3578274bc645949712a3fecea6746c2022-12-21T18:57:24ZengElsevierAlexandria Engineering Journal1110-01682020-10-0159530413047A numerical approach for solving variable order differential equations using Bernstein polynomialsNematollah Kadkhoda0Department of Mathematics, Faculty of Basic Sciences, Bozorgmehr University of Qaenat, Qaenat, IranIn this study, a numerical technique is applied to investigate solutions of linear variable order differential equations(VODEs) in fluid mechanics. We investigate variable order(VO) in the Caputo sense. Our aim is to apply Bernstein polynomials(Bps) as the basis functions and operational matrices. We calculate two types of operational matrices of Bps. Using these operational matrices the main equation can be transformed into a system of algebraic equations, which must then be solved to get approximate solutions. Some examples are provided to indicate the accuracy of the presented method.http://www.sciencedirect.com/science/article/pii/S111001682030212XCaputo derivativeBernstein polynomialsVariable order differential equations |
| spellingShingle | Nematollah Kadkhoda A numerical approach for solving variable order differential equations using Bernstein polynomials Alexandria Engineering Journal Caputo derivative Bernstein polynomials Variable order differential equations |
| title | A numerical approach for solving variable order differential equations using Bernstein polynomials |
| title_full | A numerical approach for solving variable order differential equations using Bernstein polynomials |
| title_fullStr | A numerical approach for solving variable order differential equations using Bernstein polynomials |
| title_full_unstemmed | A numerical approach for solving variable order differential equations using Bernstein polynomials |
| title_short | A numerical approach for solving variable order differential equations using Bernstein polynomials |
| title_sort | numerical approach for solving variable order differential equations using bernstein polynomials |
| topic | Caputo derivative Bernstein polynomials Variable order differential equations |
| url | http://www.sciencedirect.com/science/article/pii/S111001682030212X |
| work_keys_str_mv | AT nematollahkadkhoda anumericalapproachforsolvingvariableorderdifferentialequationsusingbernsteinpolynomials AT nematollahkadkhoda numericalapproachforsolvingvariableorderdifferentialequationsusingbernsteinpolynomials |