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

在粘性流体中，从特征函数展开的观点出发，研究了卡门-密立根积分方程在边界层和尾流场动量损失中的作用。利用线性化边界层方程的本征函数对核函数进行展开。结果，积分方程被离散为无穷多个积分关系。它们等价于用伴随特征函数加权的加权残差方程。提出了协调应变法，并取得了良好的效果。给出了坐标应变函数的变分原理。在波场方面，提出了一种新的分离自变量的方法。船后自由波用两个艾里函数表示。

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.