On the approximate evaluation of oscillatory-singular integrals.

In this paper an efficient numerical scheme is proposed for the numerical computation of the Cauchy type oscillatory integral <inline-graphic></inline-graphic>; where <italic>f</italic>(<italic>x</italic>) is a well-behaved function without having any kind of singularity in the range of integration [−1; 1]. The scheme is devised with the help of quadrature rule meant for the approximate evaluation of Cauchy principal value of integrals of the type <inline-graphic></inline-graphic>; and a quasi exact quadrature meant for the numerical integration of Filon-type integrals. The error bounds are determined and the scheme numerically verified by some standard test integrals. [ABSTRACT FROM AUTHOR]