On the solution of the double Wiener-Hopf equation involved in the quarter plane problem

Abstract

This paper provides a semi analytical procedure to factorize the two dimensional kernel involved in the quarter plane diffraction problem. The proposed method is based on the reduction of the factorization problem to the solution of a Fredholm integral equation of second kind. The solution of the Fredholm integral equation appears cumbersome since it involves two folded integrals. In order to reduce the number of the numerical unknowns a suitable representation of the W-H unknowns is proposed.