论文标题
单方面迅速降低功能的无限积分的梯形公式的新共形图
New conformal map for the trapezoidal formula for infinite integrals of unilateral rapidly decreasing functions
论文作者
论文摘要
尽管将梯形公式应用于双侧快速降低功能的无限积分时，可以达到指数收敛，但在单方面迅速降低功能的情况下，它无法实现。为了解决这个问题，Stenger提出了将共形图应用于整个的应用，以使其转变为双边快速降低功能。冈田和哈纳达修改了保形图，并为修改公式提供了严格的误差。本文提出了进一步改进的共形图，并提供了两个严格的误差界限，以改善公式。还给出了比较提出的公式和现有公式的数值示例。
While the trapezoidal formula can attain exponential convergence when applied to infinite integrals of bilateral rapidly decreasing functions, it is not capable of this in the case of unilateral rapidly decreasing functions. To address this issue, Stenger proposed the application of a conformal map to the integrand such that it transforms into bilateral rapidly decreasing functions. Okayama and Hanada modified the conformal map and provided a rigorous error bound for the modified formula. This paper proposes a further improved conformal map, with two rigorous error bounds provided for the improved formula. Numerical examples comparing the proposed and existing formulas are also given.
