论文标题
在渐近分析中产生的通风型积分的数值评估
Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis
论文作者
论文摘要
我们描述了一种评估在两个鞍点可能靠近的渐近分析中出现积分的方法。这些积分出现在光学，声学或量子力学以及广泛的特殊功能中的问题中，可以转换为通风型积分，我们使用梯形规则来数值计算这些积分。用数值示例说明了两个鞍点融合时，正交法仍然有效。
We describe a method to evaluate integrals that arise in the asymptotic analysis when two saddle points may be close together. These integrals, which appear in problems from optics, acoustics or quantum mechanics as well as in a wide class of special functions, can be transformed into Airy-type integrals and we use the trapezoidal rule to compute these integrals numerically. The quadrature method, which remains valid when two saddle points coalesce, is illustrated with numerical examples.
