论文标题
另一个不确定的集成公式
Yet another DE-Sinc indefinite integration formula
论文作者
论文摘要
基于SINC近似结合TANH变换，Haber得出了在有限间隔（-1，1）上数值无限整合的近似公式。该公式使用特殊功能来用于基础函数。相比之下，Stenger得出了另一个不使用任何特殊功能，但确实包含双重和的公式。随后，穆罕默德（Muhammad）和莫里（Mori）提出了一个公式，该公式用哈伯公式中的双指数转换代替了坦的转换。田中等人几乎同时同时。提出了另一个公式，该公式基于Stenger公式中的相同替代品。正如他们报道的那样，替代物极大地提高了哈伯和Stenger公式的收敛速度。除了上面的公式外，Stenger还基于SINC近似结合了Tanh转换，还衍生出了另一个不确定的集成公式，该公式具有优雅的矩阵矢量形式。在本文中，我们提出用Stenger的第二公式中的双指数转换来替换Tanh转换。我们提供理论分析以及数值比较。
Based on the Sinc approximation combined with the tanh transformation, Haber derived an approximation formula for numerical indefinite integration over the finite interval (-1, 1). The formula uses a special function for the basis functions. In contrast, Stenger derived another formula, which does not use any special function but does include a double sum. Subsequently, Muhammad and Mori proposed a formula, which replaces the tanh transformation with the double-exponential transformation in Haber's formula. Almost simultaneously, Tanaka et al. proposed another formula, which was based on the same replacement in Stenger's formula. As they reported, the replacement drastically improves the convergence rate of Haber's and Stenger's formula. In addition to the formulas above, Stenger derived yet another indefinite integration formula based on the Sinc approximation combined with the tanh transformation, which has an elegant matrix-vector form. In this paper, we propose the replacement of the tanh transformation with the double-exponential transformation in Stenger's second formula. We provide a theoretical analysis as well as a numerical comparison.
