We consider a Dirichlet spectral problem for second order differential operator, with piecewise constant coefficients, in domain ?? the plane R2. Here is ??????, where ? fixed bounded boundary ?, ?? curvilinear band of width O(?), and ?=??????. The density stiffness constants are ??m?t ??t respectively this band, while they 1 ?; t?1, m>2, ? small positive parameter. address asymptotic behavior,...

This paper is concerned with finding numerical solutions of a flow of ODE solutions. It describes a new method, based on Euler Backward method and interpolation, for finding solutions of autonomous problems. The special aspect is that this method is explicit, and resolves the flow with similar accuracy as Euler Backward method, even when the problem is stiff. An analysis is given of both stabil...