On the Improved Green Integral Equation applied to the Water-wave Radiation-Diffraction Problem

It is shown that irregular frequencies in the source and doublet distribution method, can be eliminated if the Green function associated with Kelvin's source of pulsating strength, is modified only in the region inside the body at the level of the undisturbed free surface. The system of the resulting Green integral equation is augmented without loss of the square-integrable property of its kernel so hat the discretisation yield N linearly independent equations for N unknown variables. From the solution, the potential and velocity at any point on the wetted surface of a surface-piercing body can be found using the properties of the double layer composed of the source and normal doublet distribution.