Optimal Collocation Nodes for Fractional Derivative Operators
Optimal Collocation Nodes for Fractional Derivative Operators
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DOI：
10.1137/140993697
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发表时间：
2014-07
期刊：
影响因子：
--
通讯作者：
L. Fatone;D. Funaro
中科院分区：
文献类型：
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作者：
L. Fatone;D. Funaro
研究了分数阶导数算子的谱离散化，其中逼近基与Jacobi多项式集有关。伪谱方法是通过假设用于表示待微分函数的网格可能与配置网格不重合来实现的。新的选择开辟了道路的替代技术的分析和搜索的最佳分布的配置节点，根据运营商被近似。一旦选择了初始表示网格，就提供了如何恢复配置网格的指示，目的是扩大近似空间的维度。作为该过程的结果，性能得到改善。最后，将其应用于分数阶对流扩散方程，并在精度和效率方面进行了比较。如分析所示，节点的特殊选择也可以建议加速计算的技巧。
Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudospectral method is implemented by assuming that the grid, used to represent the function to be differentiated, may not be coincident with the collocation grid. The new option opens the way to the analysis of alternative techniques and the search for optimal distributions of collocation nodes, based on the operator to be approximated. Once the initial representation grid has been chosen, indications for how to recover the collocation grid are provided, with the aim of enlarging the dimension of the approximation space. As a result of this process, performances are improved. Applications to fractional type advection-diffusion equation and comparisons in terms of accuracy and efficiency are made. As shown in the analysis, special choices of the nodes can also suggest tricks to speed up computations.