The main purpose of this paper is to construct a semi-implicit difference scheme for the multi-term time-fractional Burgers-type equations. Firstly, the L2-discretization formula is applied to the discretization of the multi-term Caputo fractional derivatives. Secondly, the second-order spatial derivative is approximated by using the second-order central difference quotient approximation and the nonlinear convection term \(uu_x\) is discretized via the semi-implicit method. Then, a fully discrete finite difference scheme is established. The unconditional stability and convergence in maximum-norm are derived by the discrete energy method and the mathematical induction. Numerical experiments are performed to validate the theoretical analysis.

本文的主要目的是为多元时间分数阶Burgers型方程构建一个半隐式差分格式。首先，将L2离散化公式应用于多维Caputo分数阶导数的离散化。其次，通过使用二阶中心差商近似来近似二阶空间导数，并通过半隐式方法将非线性对流项\（uu_x \）离散化。然后，建立了一个完全离散的有限差分方案。通过离散能量法和数学归纳法推导了最大范数的无条件稳定性和收敛性。进行数值实验以验证理论分析。