Discretization of Systems Possessing Attractors

Abstract

For the numerical realization of the systems possessing attractors, it is common practice to use the time and space finite difference schemes and other approximations of such systems. In essence, one deals with the replacing of an initial infinite-dimensional system by different finite dimensional systems. In connection with this the question emerges: what properties of the initial system are kept under such approximation. Since we consider the systems possessing attractors, the question must be answered first: what happens with attractors of such systems under above time-space discretization.