《Table 1:Comparison results on the absolute errors derived from LPS method and Legendre operational

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《数值求解Bagley-Torvik分数阶微分方程的局部多项式光滑因子方法（英文）》

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In Figure 3，local polynomial smoother approximates analytical solution in Example 2 with parameters n=51，p=3，h=0.1，which is much more efficient and accurate.We also solve LPS under different order p=3，4 by fixing bandwidth h=0.2，n=51 for Example 2 in Figure 4.We can find the magnitude of errors decreases to between 10 to the power of-11 and 10 to the power of-13.Table 2 gives the comparison results on the absolute errors derived from the LPS method，pseudospectral method and Adams-Bashforth method at point ti=0.0:0.2:1.0 in Example 2，which shows that the LPS method proposed is most efficient and most accurate than other two methods.