标题：Spectral methods for the time-fractional Navier-Stokes equation
作者：Zheng, Rumeng; Jiang, Xiaoyun
作者机构：[Zheng, Rumeng; Jiang, Xiaoyun] Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
通讯作者：Jiang, Xiaoyun;Jiang, XY
通讯作者地址：[Jiang, XY]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源：APPLIED MATHEMATICS LETTERS
关键词：Time-fractional Navier-Stokes equation; Fourier spectral method;; Stability and convergence
摘要：In this paper, the L1 Fourier spectral method is considered to solve the time-fractional Navier-Stokes equation with periodic boundary condition. The Fourier spectral method is employed for spatial approximation, and the L1 finite difference scheme is used to discrete the Caputo time fractional derivative. Analysis of stability and convergence are accomplished as well, leading to the conclusion that our numerical method is unconditionally stable, and the solution converges to the exact one with order O(tau(2-alpha) + N-s), where tau and N are the time step size and polynomial degree, respectively. The numerical example is provided to testify the effectiveness of our scheme, from the results of which, it turns out that the L1 Fourier spectral method is effective for solving the time-fractional Navier-Stokes equation. (C) 2018 Elsevier Ltd. All rights reserved.