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Asymptotology

About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.


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Journal ArticleDOI
TL;DR: In this article, a detailed asymptotic analysis of spectral methods for prototype problems is presented, and a number of surprising results are presented, including the O(N) boundedness of the eigenvalues of collocation on Legendre points.
Abstract: A detailed asymptotic analysis of spectral methods for prototype problems is presented. Asymptotic error behavior throughout the solution regime is given. A number of surprising results are presented, including theO(N) boundedness of the eigenvalues of collocation on Legendre points.

16 citations

Journal ArticleDOI
TL;DR: In this paper, the asymptotic stability and global stability of equilibria in autonomous systems of differential equations are analyzed in terms of compact invariant sets and positively invariants.
Abstract: The asymptotic stability and global asymptotic stability of equilibria in autonomous systems of differential equations are analyzed. Conditions for asymptotic stability and global asymptotic stability in terms of compact invariant sets and positively invariant sets are proved. The functional method of localization of compact invariant sets is proposed for verifying the fulfillment of these conditions. Illustrative examples are given.

16 citations

Book ChapterDOI
07 Jun 2004

16 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526