论文标题
在基于对称组的周期索引的新型数值正交上
On a novel numerical quadrature based on cycle index of symmetric group for the Hadamard finite-part integrals
论文作者
论文摘要
为了准确评估Hadamard的有限零件积分，本文提出了一种新型的插值型正交正交正交。在我们的方法中，数值分隔差用于表示集成函数的高阶导数，这使得基于对称组的循环指数将数值正交降低到简洁的公式中成为可能。此外，还提供了收敛分析并给出了误差估计。数值结果是在重量函数不同的情况下提出的，这些函数证实了所提出的方法的性能。
To evaluate the Hadamard finite-part integrals accurately, a novel interpolatory-type quadrature is proposed in this article. In our approach, numerical divided difference is utilized to represent the high order derivatives of the integrated function, which make it possible to reduced the numerical quadrature into a concise formula based on the cycle index for symmetric group. In addition, convergence analysis is presented and the error estimation is given. Numerical results are presented on cases with different weight functions, which substantiate the performance of the proposed method.
