Matrices of Green's type for the potential equation on a cylindrical surface joined to a hemisphere

摘要

In this study, we use a new approach to constructing Green's functions for a particular case of joined surface of revolution which is rooted in the classical method of the separation of variables. The approach was originally developed [1, 2] to construct Green's functions and matrices for homogeneous media. The first stage of our approach represents the Green's function (matrix) to be found in terms of its Fourier series with respect to one of the independent variables. Consequently, boundary value problems arise for systems of ordinary differential equations in the coefficients of the Fourier series. Green's matrices for such equations are then constructed with the help of a well-known procedure. The second stage of the approach deals with the complete summation of the singular part of the Green's function so as to be computationally effective.