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Sinc-Galerkin method for solving the time fractional convection–diffusion equation with variable coefficients
Advances in Difference Equations ( IF 4.1 ) Pub Date : 2020-09-18 , DOI: 10.1186/s13662-020-02959-5
Li Juan Chen , MingZhu Li , Qiang Xu

In this paper, a new numerical algorithm for solving the time fractional convection–diffusion equation with variable coefficients is proposed. The time fractional derivative is estimated using the \(L_{1}\) formula, and the spatial derivative is discretized by the sinc-Galerkin method. The convergence analysis of this method is investigated in detail. The numerical solution is \(2-\alpha\) order accuracy in time and exponential rate of convergence in space. Finally, some numerical examples are given to show the effectiveness of the numerical scheme.



中文翻译:

用Sinc-Galerkin方法求解变系数时间分数对流扩散方程

本文提出了一种新的求解变系数时间分数对流扩散方程的数值算法。时间分数导数使用\(L_ {1} \)公式估算,空间导数通过sinc-Galerkin方法离散化。详细研究了该方法的收敛性分析。数值解是时间的\(2- \ alpha \)精度和空间收敛的指数速率。最后,通过数值算例说明了该数值方案的有效性。

更新日期:2020-09-20
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