Author(s)

Y.A. Melnikov, K.L. Shirley & A.J. Worsey

Abstract

Matrices of Green's type for the equation of potential on joined surfaces of revolution Y.A. Melnikov, K.L. Shirley & A.J. Worsey Department of Mathematics and Statistics, Middle Tennessee State University, Murfreesboro, ABSTRACT In this study, we use a new approach for constructing Green's functions and matrices which is rooted in the classical method of the separation of variables. 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 and final stage of the approach is of considerable practical importance. It deals with either complete or partial summation of the Fourier series. This phase makes it possible to split off the regular

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