Two types of splitting algorithms are proposed for approximation of Cauchy type singular integrals having high frequency Fourier kernel. To evaluate non-singular integrals, modified Levin collocation methods with multiquadric radial basis function and Chebyshev polynomials are proposed. In the scenario of interval splitting, a multi-resolution quadrature is used to tackle the singularity ridden kernel. While in the case of integrand splitting, the singular part integral is evaluated analytically. Logarithmic singular integrals with oscillatory kernels are transformed to Cauchy principal value integrals and computed with the new algorithms. Error analysis of the component algorithms, as well as the individual methods, is performed theoretically. Validation of accuracy and error estimates of the methods are performed numerically as well.

为逼近具有高频傅立叶核的柯西型奇异积分，提出了两种分裂算法。为了评估非奇异积分，提出了具有多二次径向基函数和切比雪夫多项式的修正莱文搭配方法。在区间分裂的场景中，使用多分辨率正交来解决奇异核。而在被积函数分裂的情况下，奇异部分积分被解析计算。具有振荡核的对数奇异积分被转换为柯西主值积分并用新算法计算。组件算法以及各个方法的误差分析是在理论上进行的。方法的准确性和误差估计的验证也以数字方式进行。