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分数阶扩散方程的无网格数值模拟
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Abstract:
文章借助径向基无网格方法数值求解分数阶扩散方程，时间上使用有限差分方法离散时间导数，空间上分别选取Multi Quadrics (MQ)，Thin Plate Spline (TPS)和Cubic三种径向基函数近似未知函数，比较得出三种径向基函数的逼近精度类似，但Cubic径向基函数无须选择形状参数，数值结果验证了该方法的可行性和有效性。
In this paper, the mesh-less method based on radial basis functions is used to solve the fractional diffusion equation numerically. In terms of time, finite difference method is used to discrete time derivatives. In terms of space, three approximate unknown functions of radial basis functions of Multi Quadrics (MQ), Thin Plate Spline (TPS) and Cubic are selected respectively. The approxima-tion accuracy of three kinds of radial basis function is similar, but Cubic radial basis function does not need to select shape parameter. Numerical results demonstrate the feasibility and effectiveness of the proposed method.
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