中文摘要：

随着分数阶导数的广泛应用，分数阶偏微分方程数值算法的研究成为一个热点。采用局部径向基函数法求解二维时间分数阶扩散方程，并建立数值离散格式，讨论了影响区域的配点数、形状参数取值以及布点方式对算法精度的影响。最后给出了数值算例，数值结果表明：当影响区域点数较多时，算法精度较高，但计算量会相应地增加；当形状参数值取在一定的范围内时，该算法对参数敏感度不明显，对计算精度影响不大;在均匀布点和随机布点两种方式下，计算精度无明显区别。

英文摘要：

With the widely application of the fractional order derivative diffusion equation,the research on numerical methods for fractional partial differential equation becomes a hot issue.In this paper,a Local RBF method was introduced to solve two-dimensional time-fractional diffusion equation and the numerical formula was established.Then the accuracy of the presented method can be discussed,containing the different numbers of influence domain collocation nodes,the shape parameter and the type of collocating nodes.Finally,two numerical examples were included to illustrate that the more number of influence domain collocation nodes,the better accuracy.Whereas the amount of calculation increases.The sensitivity of the shape parameter chosen in an appropriate range is not obvious.The accuracy has no obvious difference in uniform and random collocation ways.