We study accurate and stable approximations for highly oscillatory integrals (HOIs) which are demanding in computational engineering, especially for high frequency. In literature, the Levin method with radial basis functions (RBFs) is considered for better accuracy instead of stability of the algorithm. In this work, we demonstrate an accurate and stable Levin method for a class of RBFs. In addition, hybrid functions are coupled with Levin method to compute HOIs in case of stationary point, which returns a stable splitting procedure. Furthermore, error analysis of Levin method in the context of Gaussian RBFs is obtained. Although our error analysis is not significantly improved, however, we present a stable algorithm for evaluation of HOIs. The methods are implemented for both stationary and without stationary point for low and high frequencies. In each case, we address accuracy and stability of the algorithm which is reflected in numerical experiments. The obtained results are compared with well-known methods in the literature. Also, the numerical examples show that the proposed methods are highly accurate even for high frequency.

我们研究高振荡积分（HOI）的准确和稳定的近似值，这在计算工程中尤其是在高频方面要求很高。在文献中，考虑使用具有径向基函数（RBF）的Levin方法以获得更好的精度，而不是算法的稳定性。在这项工作中，我们演示了针对一类RBF的准确且稳定的Levin方法。此外，混合函数与Levin方法结合使用以计算固定点情况下的HOI，这将返回稳定的拆分过程。此外，获得了在高斯RBFs背景下的Levin方法的误差分析。尽管我们的错误分析没有得到明显改善，但是，我们提出了一种稳定的HOI评估算法。该方法针对低频和高频针对固定点和无固定点均实现。在每种情况下，我们都针对算法的准确性和稳定性进行了研究，这体现在数值实验中。将获得的结果与文献中众所周知的方法进行比较。而且，数值示例表明，即使对于高频，所提出的方法也是高度准确的。