高振荡积分的复合中矩形公式外推算法

Approximate Calculation of High Oscillatory Integrals

振荡积分在信号处理、波动等问题中有广泛的应用。本文利用复合中矩形公式近似计算高振荡积分,并根据求积公式推导出误差渐进展开式。然后在误差渐进展开式的基础上设计外推算法。并证明了外推算法的收敛阶及其收敛速度。最后,通过数值算例验证了算法的有效性。

The oscillatory integral is widely applied in signal processing,wave propagation,and other related fields.Firstly,based on the composite midpoint rule,the high oscillatory integral was approximated,and the error asymptotic expansion was derived according to the integration formula.Then derives the asymptotic expansion of the error based on the integration formula.Nextly,based on the asymptotic expansion of the error,an extrapolation algorithm was designed.Furtherly,the convergence order and speed of the extrapolation algorithm were demonstrated.Finally,the effectiveness of the algorithm was verified through numerical examples.