This paper explores numerical techniques for evaluating a class of oscillatory infinite integrals of the form ${\int }_0^{\infty }f\left(k\right)J_m\left(k\right)J_n\left(hk\right)sin\left(t\sqrt{k}\right)\mathrm{d}k.$These oscillatory integrals arise from the transient super Green function associated with cylindrical surfaces in a multi-domain method for three-dimensional hydrodynamic problems in the time domain. The original integral is decomposed into two sub-integrals which are studied in the real $k$-axis and the complex plane, respectively. The second sub-integral is reformulated by contour integrals whose integrands are exponentially decreasing and well suited for numerical evaluation. The techniques proposed in this paper are shown to be very efficient and accurate by comparing with results from Mathematica.

本文探讨了用于评估一类形式的振荡无穷积分的数值技术 ${\int }_0^{\infty }F（ķ）{Ĵ}_{米}（ķ）{Ĵ}_{ñ}（Hķ）罪（Ť\sqrt{ķ}）\mathrm{d}ķ。$这些振荡积分是由时域中的三维流体动力学问题的多域方法中与圆柱表面相关的瞬态超格林函数产生的。原始积分被分解为两个子积分$ķ$轴和复平面。第二个子积分通过轮廓积分来重新形成，轮廓积分的被乘数呈指数递减，非常适合数值评估。通过与Mathematica的结果进行比较，可以证明本文提出的技术非常有效和准确。