Third-order wave diffraction by a truncated circular cylinder

The diffraction problem for a truncated circular cylinder is formulated up to the third order referring to the wave slope. The problem is solved by me ans of eigenfunction expansion. The Green function suitable for the pressur e distribution problem is used to give a special solution which satisfies t he inhomogeneous free-surface condition in higher-order problems. The speci al solution is expressed by an integral over the free surface and the singu larity contained in the integrand is discussed. A new method to improve the convergence of the solution is proposed, which has the advantage of simpli city compared with the previous approach. A convergence test also shows sat isfactory results. The third-order wave forces are evaluated and compared w ith the previous results.