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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
S. M. Roberts1
TL;DR: In this article, the boundary value technique is used to solve singular perturbation problems that may or may not succumb to asymptotic methods, such as the method of Carrier and Pearson.
Abstract: Singular perturbation problems not amenable to solution by asymptotic methods require special treatment, such as the method of Carrier and Pearson. Rather than devising special methods for these problems, this paper suggests that there may be a uniform way to solve singular perturbation problems, which may or may not succumb to asymptotic methods. A potential mechanism for doing this is the author's boundary-value technique, a nonasymptotic method, which previously has only been applied to singular perturbation problems that lend themselves to asymptotic techniques. Two problems, claimed by Carrier and Pearson to be insoluble by asymptotic methods, are solved by the boundary-value method.

3 citations

Journal ArticleDOI
TL;DR: The asymptotic behaviour of the solution to the coupled system of transport equations and their diffusion approximations introduced in [5] and the rate of the asymPTotic decay are studied.
Abstract: In this paper we study the asymptotic behaviour of the solution to the coupled system of transport equations and their diffusion approximations introduced in [5]. We also give the rate of the asymptotic decay. This analysis is based in an essential way on the methods we introduced in [3,4].

3 citations

Book ChapterDOI
01 Jan 1986
TL;DR: In this article, the authors established the asymptotic behavior of a class of discrete solutions of the Burgers' Equation and discussed the role of smoothing and filtering and the need of computing near some (hR)opt.
Abstract: Based on a Nonlinear Equivalence Theorem and a general method of error analysis, we established the asymptotic behavior of a class of discrete solutions of the Burgers’ Equation. As a model of fluid flow equations in CFD, we discussed the role of smoothing and filtering and the need of computing near some (hR)opt. for reasonable asymptotic approximations.

3 citations

Journal ArticleDOI
TL;DR: In this article, the limiting equations approach is applied to study the stability properties with respect to a part of the state variables for non-autonomous dynamical systems, and sufficient conditions are given for uniform asymptotic eventual strongly partial stability.
Abstract: In this paper the limiting equations approach is applied to study the stability properties with respect to a part of the state variables for nonautonomous dynamical systems. Sufficient conditions are given for uniform asymptotic eventual strongly partial stability and for uniform asymptotic partial stability. An application of the results is given.

3 citations

Posted Content
TL;DR: In this paper, various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. But they do not consider the non-local interaction between variables of the discrete media into account.
Abstract: In this lectures various methods which give a possibility to extend an area of applicability of perturbation series and hence to omit their local character are analysed. While applying asymptotic methods as a rule the following situation appears: the existence of asymptotics for $\ve\rightarrow 0$ implies an existence of the asymptotics for $\ve\rightarrow\infty$. Therefore, the idea to construct one function valid for the whole parameter interval for $\ve$ is very attractive. The construction of asymptotically equivalent functions possessing a known asymptotic behaviour for $\ve\rightarrow 0$ and $\ve\rightarrow \infty$ will be discussed. Using summation and interpolation procedures we focus on continuous models derived from a discrete micro-structure. Various continualization procedures that take the non-local interaction between variables of the discrete media into account are analysed.

3 citations


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