Аппроксимации Паде и континуализация для одномерной цепочки масс

Abstract

Various continuous models (CM) for 1D discrete media are under consideration. As example the difference-differential equation, describing a system of connected oscillators, is chosen. String-type approximation shows excellent results for low part of frequency spectra, but for forced oscillations the corresponding mistake can be very big. So, the more appropriate CM should be found. We analyze three following models: the intermediate CM are obtained by replacing the difference operator (DO) for the derivative operator of the order 2k, k > 1; the quasi-CM are more accurate approximations of the DO via Pade approximates (PA); the two-point PA give the most precise results. Possibilities of the approach generalization and application are discusse