In this study, a new unconventional approach that departs from the classical method is proposed to solve the modified scalar Wiener–Hopf equation of the third kind with regard to the diffraction problem of cylindrical waves caused by perfectly conducting successive step discontinuities. This novel technique allows for the asymptotic analytical evaluation of the branch-cut integrals appearing in the approximate iterative solution of a pair of coupled Fredholm integral equations of the second kind, into which the corresponding Wiener–Hopf equation is reduced. The results obtained using this new method are compared to those of the classical method by graphically presenting the amplitude of the diffracted field with respect to certain significant parameters, such as the width and height of the steps.
Durgut et al. (Thu,) studied this question.