  Spline Galerkin methods for the double layer potential equation on contours
with corners are studied. The stability of the method depends on the
invertibility of some operators $R_{\tau}$ associated with the corner points
$\tau$. The operators $R_{\tau}$ do not depend on the shape of the contour but
only on the opening angles of the corner points $\tau$. The invertibility of
these operators is studied numerically via the stability of the method on model
curves, all corner points of which have the same opening angle. The case of the
splines of order $0,1$ and $2$ is considered. It is shown that no opening angle
located in the interval $[0.1\pi,1.9\pi]$ can cause the instability of the
method. This result is in strong contrast with the Nystr{\"o}m method, which
has four instability angles in the interval mentioned. Numerical experiments
show a good convergence of the methods even if the right-hand side of the
equation has discontinuities located at the corner points of the contour.
