This paper presents a meshless finite point method (FPM) for the numerical analysis of the fractional cable equation. A second-order time discrete scheme is proposed to approximate both integer-order and fractional-order time derivatives. Then, based on the stabilized moving least squares approximation and the meshless smoothed gradients, a new implementation of the FPM is provided to enhance the accuracy and convergence rate in space. Theoretical error of the FPM is analyzed. Numerical results verify the efficiency of the method and show that the method can gain second-order accuracy in time and fourth-order accuracy in space.

中文翻译：

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一种使用无网格平滑梯度的分数索方程的有限点方法

本文提出了一种用于分数电缆方程数值分析的无网格有限点法 (FPM)。提出了一种二阶时间离散方案来近似整数阶和分数阶时间导数。然后，基于稳定的移动最小二乘近似和无网格平滑梯度，提供了一种新的 FPM 实现，以提高空间的准确性和收敛速度。分析了FPM的理论误差。数值结果验证了该方法的有效性，表明该方法可以在时间上获得二阶精度，在空间上获得四阶精度。