  This article considers the problem of diffraction by a wedge consisting of
two semi-infinite periodic arrays of point scatterers. The solution is obtained
in terms of two coupled systems, each of which is solved using the discrete
Wiener--Hopf technique. An effective and accurate iterative numerical procedure
is developed to solve the diffraction problem, which allows us to compute the
interaction of thousands of scatterers forming the wedge. A crucial aspect of
this numerical procedure is the effective truncation of slowly convergent
single and double infinite series, which requires careful asymptotic analysis.
A convergence criteria is formulated and shown to be satisfied for a large
class of physically interesting cases. A comparison to direct numerical
simulations is made, highlighting the accuracy of the method.
