Integral Equation for the Finite Depth Green Function at Surface

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We want to solve

[math] \phi(x) = \int_{-L}^{L}G(x,\xi) \left( \alpha\phi(\xi) - w(\xi) \right)\mathrm{d} \xi [/math]

where [math]G(x,\xi)[/math] is the Free-Surface Green Function for two-dimensional waves, with singularity at the water surface. We break the surface into [math]N[/math] evenly spaced point [math]x_n = -L = hn[/math] where [math]h=2L/N[/math] and [math]n=0,1,\dots,N[/math]

Matlab Code

A program to calculate the coefficients for the semi-infinite dock problems can be found here matrix_G_surface.m

Additional code

This program requires