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

摘要

The local polynomial smoother (LPS) method is proposed in this paper to derive the numerical solution of the Bagley-Torvik fractional-order differential equations. Firstly, the local polynomial smoother method is well constructed and its main thinking is emphasized. Then this method is employed to solve the Bagley-Torvik FDEs. Finally, some numerical comparison experiments with some other methods are made to demonstrate that the LPS method proposed is more efficient and more accurate than Legendre operational matrix method and pseudo-spectral method.%为了得到Bagley-Torvik分数阶微分方程的数值解,我们提出了局部多项式光滑因子(LPS)方法.首先,我们构建了LPS方法,重点强调了该方法的主要思想.然后,用该方法数值求解Bagley-Torvik分数阶微分方程.数值实验表明:该方法比Legendre运算矩阵方法和伪谱方法更加有效更加精确.