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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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01 Jan 2008
TL;DR: In this article, an analysis of dispersive/dissipative features of the difference schemes used for simulations of the non-linear Burgers' equation is developed based on the travelling wave asymptotic solutions of its differential approximation.
Abstract: An analysis of dispersive/dissipative features of the difference schemes used for simulations of the non-linear Burgers' equation is developed based on the travelling wave asymptotic solutions of its differential approximation. It is shown that these particular solutions describe well deviations in the shock profile even outside the formal applicability of the asymptotic expansions, namely for shocks of moderate amplitudes. Analytical predictions may be used to improve calculations by suitable choice of the parameters of some familiar schemes, i.e., the Lax-Wendroff, Mac-Cormack etc. Moreover, an improvement of the scheme may be developed by adding artificial terms according to the asymptotic solution.

5 citations

Journal ArticleDOI
TL;DR: In this paper, the authors continue the factorizational theory of asymptotic expansions of type (*),,, where the expansion is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x 0.
Abstract: Part II-B of our work continues the factorizational theory of asymptotic expansions of type (*) , , where the asymptotic scale , , is assumed to be an extended complete Chebyshev system on a one-sided neighborhood of x0. The main result states that to each scale of this type it remains as-sociated an important class of functions (namely that of generalized convex functions) enjoying the property that the expansion (*), if valid, is automatically formally differentiable n ? 1 times in the two special senses characterized in Part II-A. A second result shows that formal applications of ordinary derivatives to an asymptotic expansion are rarely admissible and that they may also yield skew results even for scales of powers.

5 citations

Journal ArticleDOI
TL;DR: A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered in this paper, and the existence of exact solutions which have these exact solutions has been proved.
Abstract: A family of asymptotic solutions at infinity for the system of ordinary differential equations is considered. Existence of exact solutions which have these asymptotics is proved.

5 citations


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