Numerical evaluation of oscillatory-singular integrals. Issue 12 (2nd December 2019) - Yang, Gang; Yao, Luogen; Chen, Ruyun
ABSTRACT: In this paper, we consider an asymptotic Filon-type method for computing the oscillatory Cauchy principal value integrals and end-point oscillatory-singular integrals. The method is constructed by using a Lagrange interpolating polynomial to approximate the non-oscillatory function so that it successfully avoids the singularity and solving the systems of equations. Numerical examples and theoretical results show the accuracy and efficiency of the proposed method.