On the Stability of a Class of Finite-Difference Equations with Slowly Varying Coefficients

摘要

Linear equations with constant coefficients are one of the few classes (and probably the only one) in which the stability problem can be solved completely. In this connection, various approaches like perturbation theory, which permit one to reduce the stability analysis of arbitrary equations to the study of equations with constant coefficients, are important (e.g., see [1-3]). One of such approaches is considered in the present paper.