期刊
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
卷 264, 期 -, 页码 163-177出版社
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2013.05.012
关键词
Rayleigh-Stokes problem; High-order compact finite difference; Fourier analysis; Unconditional stability and convergence; RBF meshless approach; Collocation and Kansa's method
资金
- University of Kashan [258499/2]
This article is devoted to the comparison between a high order difference scheme and radial basis functions (RBFs) meshless approach for the numerical solution of two-dimensional fractional Rayleigh-Stokes problem. The fractional derivative of problem is described in the Riemann-Liouville sense. In the high order difference scheme we discretize the spaces derivatives with a fourth-order compact scheme and use the Grunwald-Letnikov discretization of the Riemann-Liouville derivatives to obtain a fully discrete implicit scheme. Also in the RBF meshless method we discretize the time fractional derivatives of the mentioned equation by integrating both sides of it then we will use the Kansas approach to approximate the spatial derivatives. We prove the stability and convergence for high order difference scheme using Fourier analysis and for time-discrete scheme in RBF method via energy approach. We compare the results of compact finite difference method and RBF meshless approach in terms of accuracy and CPU time. Also we compare the numerical results of compact difference scheme with other methods in the literature to show the high accuracy and efficiency of the proposed method. (C) 2013 Elsevier B.V. All rights reserved.
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