Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis

Bessel、Hankel 和 Airy 函数的数值计算

Numerical calculation of Bessel, Hankel and Airy functions

针对大阶大参数 Bessel/Hankel 函数数值计算的难题，提出结合 Debye 多项式、Airy 函数 Stokes 线处理及非线性序列变换重求和均匀渐近展开的算法，扩展了现有方法的适用范围。

抛物柱面函数的数值与渐近性质

Numerical and Asymptotic Aspects of Parabolic Cylinder Functions

本文改进Olver的抛物柱面函数一致渐近展开，用初等函数和Airy函数表示，扩大数值算法适用区间，并给出三组展开的数值测试。

A numerical method for oscillatory integrals with coalescing saddle points

The value of a highly oscillatory integral is typically determined asymptotically by the behaviour of the integrand near a small number of critical points. These include the endpoints of the integration domain and the so-called stationary points or saddle points -- roots of the derivative of the phase of the integrand -- where the integrand is locally non-oscillatory. Modern methods for highly oscillatory quadrature exhibit numerical issues when two such saddle points coalesce. On the other hand, integrals with coalescing saddle points are a classical topic in asymptotic analysis, where they g…

非线性边值问题的数值方法：物理海洋学中的应用

Numerical Methods for a Nonlinear BVP Arising in Physical Oceanography

本文比较了三种海洋环流模型的数值结果，指出准均匀网格方法最易实现，而自由边界方法比传统截断边界方法更可靠。