In this paper, a stabilized numerical method with high accuracy is proposed to solve time-fractional singularly perturbed convection-diffusion equation with variable coefficients. The tailored finite point method (TFPM) is adopted to discrete equation in the spatial direction, while the time direction is discreted by the G-L approximation and the L1 approximation. It can effectively eliminate non-physical oscillation or excessive numerical dispersion caused by convection dominant. The stability of the scheme is verified by theoretical analysis. Finally, one-dimensional and two-dimensional numerical examples are presented to verify the efficiency of the method.

中文翻译：

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求解时间分数对流主导的扩散方程的新型有限点方法

本文提出了一种高精度的稳定数值方法来求解变分时变分数阶奇异摄动对流扩散方程。在空间方向上离散方程采用量身定制的有限点法（TFPM），而通过GL近似和L1近似来离散时间方向。它可以有效消除由对流占主导地位的非物理振荡或过度的数值离散。理论分析验证了该方案的稳定性。最后，通过一维和二维数值算例验证了该方法的有效性。