The modified Filon–Clenshaw–Curtis rules, proposed earlier by the author, are combined with the (double) exponential transformations in such a way that (1) the necessity of computing the inverse of the oscillator function is released, (2) possible inaccuracy due to rounding error, when the amplitude function has endpoint singularities, is treated, (3) difficulties raised by the stationary points of the oscillator function are treated, and (4) all the benefits of the original Filon–Clenshaw–Curtis rules are preserved. We also carry out some numerical experiments, which illustrate the efficiency of the proposed algorithms while earlier methods based on Filon–Clenshaw–Curtis rules result in poor approximations or even fail.

作者先前提出的修改后的Filon-Clenshaw-Curtis规则与（双）指数变换相结合，使得（1）释放了计算振荡器函数逆的必要性，（2）可能的不准确性由于舍入误差，当振幅函数具有端点奇点时，将予以处理；（3）处理由振荡器函数的固定点引起的困难；（4）保留原始的Filon–Clenshaw–Curtis规则的所有优点。我们还进行了一些数值实验，这些实验说明了所提出算法的效率，而基于Filon–Clenshaw–Curtis规则的早期方法会导致近似值不理想甚至失败。