Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain
Fast exponential time differencing/spectral-Galerkin method for the nonlinear fractional Ginzburg-Landau equation with fractional Laplacian in unbounded domain
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DOI：
10.1016/j.aml.2020.106710
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发表时间：
2021-02
期刊：
影响因子：
--
通讯作者：
Pengde Wang
中科院分区：
文献类型：
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作者：
Pengde Wang
本文提出了一种快速有效的谱伽辽金方法，用于处理涉及 R d 中分数拉普拉斯算子的非线性复数 Ginzburg-Landau 方程。通过采用类傅立叶双正交映射切比雪夫函数作为基函数，分数拉普拉斯可以完全对角化。然后，对于所得到的对角化半离散系统，提出了指数时间差分方案来进行时间离散化。所获得的方法能够快速实现，并且在时间上具有二阶精度，在空间上具有代数精度。通过一维和二维数值算例的测试来验证该方法的准确性和效率。
This paper proposes a fast and efficient spectral-Galerkin method for the nonlinear complex Ginzburg–Landau equation involving the fractional Laplacian in R d. By employing the Fourier-like bi-orthogonal mapped Chebyshev function as basis functions, the fractional Laplacian can be fully diagonalized. Then for the resulting diagonalized semi-discrete system, an exponential time differencing scheme is proposed for the temporal discretization. The obtained method can be fast implemented and has second order accuracy in time and algebraical accuracy in space. One-and two-dimensional numerical examples are tested to validate the accuracy and efficiency of the proposed method.