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Solving the Basset equation via Chebyshev collocation and LDG methods | ||
| Journal of Mathematical Modeling | ||
| دوره 9، شماره 1، فروردین 2021، صفحه 61-79 اصل مقاله (583.88 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2020.17135.1489 | ||
| نویسندگان | ||
| Mohammad Izadi1؛ Mehdi Afshar* 2 | ||
| 1Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran | ||
| 2Department of Mathematics and Statistics, Zanjan Branch , Islamic Azad University, Zanjan, Iran. | ||
| چکیده | ||
| Two different numerical methods are developed to find approximate solutions of a class of linear fractional differential equations (LFDEs) appearing in the study of the generalized Basset force, when a sphere sinks in a viscous fluid. In the first one, using the Chebyshev bases, the collocation points, and the matrix operations, the given LFDE reduces to a matrix equation while in the second one, we employ the local discontinuous Galerkin (LDG) method, which uses the natural upwind flux yielding a stable discretization. Unlike the first method, in the latter method we are able to solve the problem element by element locally and there is no need to solve a full global matrix. The efficiency of the proposed algorithms are shown via some numerical examples. | ||
| کلیدواژه‌ها | ||
| Basset equation؛ Caputo fractional derivative؛ Chebyshev polynomials؛ Collocation method؛ Local discontinuous Galerkin method؛ Numerical stability | ||
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