Using iteration to solve n by n matrix Wiener-Hopf equations involving exponential factors with numerical implementation

Wiener-Hopf equations involving $n\times n$ matrices can arise when solving mixed boundary value problems with $n$ junctions at which the boundary condition to be imposed changes form.  The offset Fourier transforms of the unknown boundary values lead to exponential factors which require careful consideration when applying the Wiener-Hopf technique. We consider the generalisation of an iterative method introduced recently (Kisil 2018) from $2\times 2$ to $n\times n$ problems. This may be effectively implemented numerically by employing a spectral method to compute Cauchy transforms. We illustrate the approach through various examples of scattering from collinear rigid plates and consider the merits of the iterative method relative to alternative approaches to similar problems.