This paper develops a two-level fourth-order scheme for solving time-fractional convection-diffusion-reaction equation with variable coefficients subjected to suitable initial and boundary conditions. The basis properties of the new approach are investigated and both stability and error estimates of the proposed numerical scheme are deeply analyzed in the $L^{\infty}(0,T;L^{2})$-norm. The theory indicates that the method is unconditionally stable with convergence of order $O(k^{2-\frac{\lambda}{2}}+h^{4})$, where $k$ and $h$ are time step and mesh size, respectively, and $\lambda\in(0,1)$. This result suggests that the two-level fourth-order technique is more efficient than a large class of numerical techniques widely studied in the literature for the considered problem. Some numerical evidences are provided to verify the unconditional stability and convergence rate of the proposed algorithm.

翻译：本文发展了一种两级第四阶级方案,以解决时间不规则的对流-扩散-反应等式,并附有受适当初始和边界条件制约的可变系数。对新办法的基础特性进行了调查,对拟议数字办法的稳定性和误差估计都进行了深入的分析,在$L ⁇ infty}(0,T;L ⁇ 2})-norm中进行了深入分析。理论表明,该方法与美元(k ⁇ 2-\frac=lambda ⁇ 2 ⁇ h ⁇ 4}(美元)的趋同无条件稳定,其中美元和美元是时间步骤和网位大小,美元是拉姆巴达因(0,1美元)。这一结果表明,两阶四阶级技术比文献中为所考虑的问题广泛研究的一大批数字技术更有效。提供了一些数字证据,以核实拟议的算法的无条件稳定性和汇合率。