数值积分的相位滞后灵敏度分析
Phase Lag Sensitivity Analysis for Numerical Integration
AI总结：
提出一种基于相位滞后函数一阶导数在拟合频率处为零的新技术，改进指数拟合数值方法在振荡问题中的性能。
摘要：
在数值积分领域，专门针对振荡函数调优的方法具有重要的实际意义。这类方法在自然科学的各个分支，特别是物理学中都是必需的，因为许多物理现象表现出明显的振荡行为。其中，用于构建振荡问题高效方法的最重要工具之一是指数（三角）拟合。这些方法的基本特征是其相位滞后在预定义频率处为零。在这项工作中，我们引入了一种新工具，改进了指数拟合数值方法的性能。新技术基于相位滞后函数在拟合频率处的一阶导数为零。文中证明，这些方法在振荡问题中表现出改进的特性。
英文摘要：
In the field of numerical integration, methods specially tuned on oscillating functions, are of great practical importance. Such methods are needed in various branches of natural sciences, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior. Among others, probably the most important tool used to construct efficient methods for oscillatory problems is the exponential (trigonometric) fitting. The basic characteristic of these methods is that their phase lag vanishes at a predefined frequency. In this work, we introduce a new tool which improves the behavior of exponentially fitted numerical methods. The new technique is based on the vanishing of the first derivatives of the phase lag function at the fitted frequency. It is proved in the text that these methods present improved characteristics in oscillatory problems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
