This paper is concerned with the numerical approximation of the time fractional Burgers equation with nonsmooth solutions. A nonlinear fully discrete scheme is presented based on the nonuniform Alikhanov formula of the Caputo time fractional derivative and Fourier spectral approximation in space. The solvability of the scheme is proved by the fixed point theorem and a priori estimate. Using the error estimation method, the proposed scheme is stable and convergent with order $O({\tau }^{\min \{\gamma \sigma ,2\}}+N^{1-m})$, where $\tau ,N,\gamma ,m$ and σ are the maximum time step size, polynomial degree, grading parameter, spatial regularity and temporal regularity parameter of the exact solution, respectively. A numerical example is performed to support the theoretical results.

本文涉及具有非光滑解的时间分数 Burgers 方程的数值逼近。基于Caputo时间分数阶导数的非均匀Alikhanov公式和空间傅里叶谱近似，提出了一种非线性完全离散方案。该方案的可解性由不动点定理和先验估计证明。使用误差估计方法，所提方案稳定且阶次收敛$哦({\tau }^{\mathrm{分钟}\{\gamma \sigma ,2\}}+N^{1-米})$， 在哪里 $\tau ,N,\gamma ,米$和σ是最大时间步长，多项式度，分级参数，空间规则性和精确解的时间规律性参数，分别。一个数值例子被执行以支持理论结果。