高振荡积分的常见数值算法研究
Study on Common Numerical Algorithms for Highly Oscillatory Integrals
DOI: 10.12677/aam.2026.158336, PDF,    科研立项经费支持
作者: 彭小蓉*, 黄仁敏, 潘 瑶：贵州师范学院数学与大数据学院，贵州 贵阳
关键词: 高振荡积分；渐近方法；Levin方法；数值最速下降法；Highly Oscillatory Integrals； Asymptotic Method； Levin Method； Numerical Steepest Descent Method
摘要: 高振荡积分广泛存在于电磁散射、量子力学、流体力学、信号处理等科学与工程领域。由于被积函数的高频振荡特性，传统数值积分方法计算成本过高而难以实用。本文系统介绍了渐近方法、Levin方法、数值最速下降法等高振荡积分的高效计算方法，为相关领域的研究者提供有意义的参考。
Abstract: Highly oscillatory integrals are widely encountered in scientific and engineering fields such as electromagnetic scattering, quantum mechanics, fluid mechanics, and signal processing. Due to the high-frequency oscillatory nature of the integrand, traditional numerical integration methods are often prohibitively expensive and thus impractical. This paper systematically introduces efficient computational methods for highly oscillatory integrals, including the asymptotic method, the Levin method, and the numerical steepest descent method, aiming to provide a useful reference for researchers in related fields.
文章引用：彭小蓉, 黄仁敏, 潘瑶. 高振荡积分的常见数值算法研究[J]. 应用数学进展, 2026, 15(8): 93-102. https://doi.org/10.12677/aam.2026.158336

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