Conference publications

Abstracts

XVII conference

Attractor of difference scheme

Ipatova V.M., Kholodov V.S.

Russia, 141700, Dolgoprudny, Moscow Region, 9 Institutsky per.,Phone: (495)408-81-72, fax: (495)576-51-55,

Attractor of evolution system is set, which is attracted by solution of system with time tending to infinity. Initially, attractors were considered only for autonomous equations, but later this concept was introduced to non-autonomous evolution problems. One question here that is important for applications is the closeness of the attractors for discrete approximations to mathematical models and the genuine attractors occurring in these models. For non-autonomous equations this problem was considered in [1], where it was proved that the uniform attractors of family of semiprocesses depend upper semicontinuosly on the parameter.

The aim of the present paper is to consider Lorentz’s system with limited vector of external forces continuosly depending on the time. Differential equations are approximated by explicit finite-difference scheme. It is proved, that considered numerical scheme has uniform attractor, and under the tending step of grid to zero its attractor belong to arbitrary close environment of genuine attractor of differential system.

This research was carried out with the support of goal-oriented program «Scientific and scientific-educational personnel of innovative Russia» for 2009-2013 years.

Bibliography.

1. Ipatova V.M. Attroctors of approximations non-autonomous evolution equations // Mathematical collection, 1997, V. 188, №6, pages 47-56.

• view as PDF