Solving the Basset equation via Chebyshev collocation and LDG methods

Document Type : Research Article

Authors

1 Department of Applied Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

2 Department of Mathematics and Statistics, Zanjan Branch , Islamic Azad University, Zanjan, Iran.

Abstract

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.

Keywords

Journal of Mathematical Modeling
Volume 9, Issue 1
January 2021
Pages 61-79

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