A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation
Abstract In this paper, a fast multiscale Galerkin algorithm is developed for solving the boundary value problem of the fractional Bagley–Torvik equation. For this purpose, we employ multiscale orthogonal functions having vanishing moments as the basis of the trial space, and we propose a truncation...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-05-01
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| Series: | Boundary Value Problems |
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| Online Access: | http://link.springer.com/article/10.1186/s13661-020-01391-8 |
| _version_ | 1831668968547418112 |
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| author | Jian Chen |
| author_facet | Jian Chen |
| author_sort | Jian Chen |
| collection | DOAJ |
| description | Abstract In this paper, a fast multiscale Galerkin algorithm is developed for solving the boundary value problem of the fractional Bagley–Torvik equation. For this purpose, we employ multiscale orthogonal functions having vanishing moments as the basis of the trial space, and we propose a truncation strategy for the coefficient matrix of the corresponding discrete system which leads to a fast algorithm. We show the algorithm has nearly linear computational complexity (up to a logarithmic factor). Numerical experiments are presented to illustrate the efficiency, accuracy and convergence of the proposed algorithm. Also, comparisons with some other existing methods are made to confirm the reliability of the algorithm |
| first_indexed | 2024-12-19T22:49:48Z |
| format | Article |
| id | doaj.art-d6b117474fba430589680fed8a0b7979 |
| institution | Directory Open Access Journal |
| issn | 1687-2770 |
| language | English |
| last_indexed | 2024-12-19T22:49:48Z |
| publishDate | 2020-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Boundary Value Problems |
| spelling | doaj.art-d6b117474fba430589680fed8a0b79792022-12-21T20:02:51ZengSpringerOpenBoundary Value Problems1687-27702020-05-012020111310.1186/s13661-020-01391-8A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equationJian Chen0School of Mathematics and Big Data, Foshan UniversityAbstract In this paper, a fast multiscale Galerkin algorithm is developed for solving the boundary value problem of the fractional Bagley–Torvik equation. For this purpose, we employ multiscale orthogonal functions having vanishing moments as the basis of the trial space, and we propose a truncation strategy for the coefficient matrix of the corresponding discrete system which leads to a fast algorithm. We show the algorithm has nearly linear computational complexity (up to a logarithmic factor). Numerical experiments are presented to illustrate the efficiency, accuracy and convergence of the proposed algorithm. Also, comparisons with some other existing methods are made to confirm the reliability of the algorithmhttp://link.springer.com/article/10.1186/s13661-020-01391-8Fast multiscale algorithmMatrix truncationCaputo fractional derivativeFractional Bagley–Torvik equation |
| spellingShingle | Jian Chen A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation Boundary Value Problems Fast multiscale algorithm Matrix truncation Caputo fractional derivative Fractional Bagley–Torvik equation |
| title | A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation |
| title_full | A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation |
| title_fullStr | A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation |
| title_full_unstemmed | A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation |
| title_short | A fast multiscale Galerkin algorithm for solving boundary value problem of the fractional Bagley–Torvik equation |
| title_sort | fast multiscale galerkin algorithm for solving boundary value problem of the fractional bagley torvik equation |
| topic | Fast multiscale algorithm Matrix truncation Caputo fractional derivative Fractional Bagley–Torvik equation |
| url | http://link.springer.com/article/10.1186/s13661-020-01391-8 |
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