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Тезисы докладов

Численное решение дифференциальных и интегральных уравнений

For a semigroup ${S_{lambda_0}(t,cdot)}$ in a Banach space $X$ corresponding, for example, to a evolution equation and having global attractor ${cal M}^{lambda_0}$ the globally stable approximation (GSA) schemes are studied. GSA scheme has attractor ${cal M}^lambda$ and in addition ${cal M}^lambdarightarrow {cal M}^{lambda_0}$ when the approximation parameters $lambda$ tend to a limit $lambda_0$. An approach to verify continuity of a global attractor of a semidynamical system with a parameter and to approximate a global attractor of a semidynamical system with error estimates in Hausdorff metric is presented. This approach is based on the properties of a function of rate of attraction to an attractor and on some new results for an unstable manifold in a neighborhood of an essential nonhyperbolical point. The current algorithm was tested on a parallel computer under a T-system for the Lorenz and for the Chafee-Infante problems. A T-system is a modern programming environment for a parallel computers and clusters which provides dynamic parallelization of programs written in a simple extension of C language. The original sequential C-program for attractor computation achieves efficient parallelization on 32-processor Linux cluster after insertion of a little amount of TC programming language keywords.

Примечание. Тезисы докладов публикуются в авторской редакции

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