Eigenvalue problems of non self-adjoint equation in the field of the ship hydrodynamics and its application to the optimum discretization method

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On the viscous fluid, Karman-Millikan's integral equations on the momentum loss in boundary layer and wake field were investigated from the viewpoint of the eigenfunction expansion. The kernel function were expanded by using the eigenfunction of the linearlized boundary layer equation. As a result, the integral equation wase discretized to infinite number of integral relations. Those ware equivalent to the Weighted residual equations weighted by the adjoint eigenfunctions. Coordinate straining method was developed and good results were obtained. Variational principle on the coordinate straining function was shown. On the wave field, new method of the separation of independent variables was presented. The free wave behind a ship was represented by the two Airy's functions.