A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions
A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions
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DOI：
10.1016/j.aml.2020.106247
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发表时间：
2020-06
期刊：
影响因子：
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通讯作者：
Rumeng Zheng;Fawang Liu;Xiaoyun Jiang
中科院分区：
文献类型：
--
作者：
Rumeng Zheng;Fawang Liu;Xiaoyun Jiang
本文考虑梯度网格上的Legendre谱方法求解具有非光滑解的二维多项时间分数阶扩散方程。渐变网格上的L1方法是在时间方向上发展的。在空间方向上，我们选择了勒让德谱方法。借助数学归纳法，从理论上证明了该方法的稳定性和收敛性。为了提高计算效率，我们在数值实现中使用了快速算法。数值结果验证了理论分析的正确性和方法的有效性。
In this paper, we consider a Legendre spectral method on graded meshes for solving the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions. The L1 method on graded meshes is developed in temporal direction. In the spatial direction, we choose the Legendre spectral method. With the help of mathematical induction method, the stability and convergence of the above mentioned method are theoretically proved. To improve the computational efficiency, we use the fast algorithm in the numerical implementation. Some numerical results are provided to verify the theoretical analysis and demonstrate the effectiveness of our method.