y''=f(x,y)的指数拟合对称多步法的相位性质
Phase properties of exponentially-fitted symmetric multistep methods for y''=f(x,y)
AI总结：
本文通过推导相位滞后误差的简洁表达式，定量分析了指数拟合对称多步法在求解y''=f(x,y)时的相位性质，从而评估不同EF版本的精度。
摘要：
获得专门针对振荡函数调谐的数值方法的一个便捷工具是指数拟合。这类方法在自然科学的各个分支中都是必需的，特别是在物理学中，因为许多物理现象表现出明显的振荡行为。针对y''=f(x,y)已经发展了许多指数拟合（EF）对称多步法。为了了解其精度，我们检查了它们的相位性质。定理2中获得的相位滞后误差的极其简单的表达式允许对每个EF版本的优点进行定量结论。
英文摘要：
A convenient tool to obtain numerical methods specially tuned on oscillating functions is exponential fitting. Such methods are needed in various branches of natural sciences, particularly in physics, since a lot of physical phenomena exhibit a pronounced oscillatory behavior. Many exponentially-fitted (EF) symmetric multistep methods for y''=f(x,y) are already developed. To have an idea of the accuracy we examine their phase properties. The remarkably simple expression of the phase-lag error obtained in Theorem 2 allows to draw quantitative conclusions on the merits of each EF version.
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