Topic
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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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
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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
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16 citations