Solving spectral problems in piecewise homogeneous media

The problems of finding natural oscillation frequencies of heterogeneous waveguides and intricately shaped membranes are studied. A numerical-and-analytic method is proposed, which consists in developing a solution in each subregion as a series in basis functions followed by matching on the boundary lines. The results of particular computations are presented. Bibliography: 3 titles. Translated fromObchyslyuval’na ta Prykladna Matematyka, No. 76, 1992, pp. 111–118.