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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, the authors introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales, which is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid expansion.
Abstract: In this paper we introduce a new technique to obtain the slow-motion dynamics in nonequilibrium and singularly perturbed problems characterized by multiple scales. Our method is based on a straightforward asymptotic reduction of the order of the governing differential equation and leads to amplitude equations that describe the slowly-varying envelope variation of a uniformly valid asymptotic expansion. This may constitute a simpler and in certain cases a more general approach toward the derivation of asymptotic expansions, compared to other mainstream methods such as the method of Multiple Scales or Matched Asymptotic expansions because of its relation with the Renormalization Group. We illustrate our method with a number of singularly perturbed problems for ordinary and partial differential equations and recover certain results from the literature as special cases.

4 citations

Journal ArticleDOI
TL;DR: A new heuristic technique of ''meta-expansions'', which is both simple and efficient in practice, even though the answers are not guaranteed to be correct in general.

4 citations

Journal Article
TL;DR: In this article, the boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.
Abstract: The boundary value problem of a class of singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters is considered.Under some suitable conditions,a formal asymptotic expansion of the solution is constructed.By using the fixed theorem,the existence and asymptotic behavior of the solution are studied.

4 citations

Book ChapterDOI
01 Jan 1994
TL;DR: The relationship between the existence of self-similar asymptotic solutions of Einstein's equations and equations of state is investigated in this paper, where it is shown that if the spacetime is selfsimilar, then the resulting equations must be of this same dimensionless form.
Abstract: The relationship between the existence of self-similar asymptotic solutions of Einstein’s equations and equations of state is investigated. For instance, imperfect fluid Bianchi models with ‘dimensionless’ equations of state are shown to have self-similar asymptotic solutions. Conversely, it is also shown that if the spacetime is self-similar, then the resulting equations of state must be of this same ‘dimensionless’ form. The conditions under which solutions are asymptotically self-similar are discussed, and it is noted that this is not a generic property of Einstein’s equations.

4 citations

Journal ArticleDOI
TL;DR: Some asymptotic estimates of the θ-methods with constant stepsize discretization are given and this gives an upper bound estimate of the solution for the long-time behaviour of the numerical solutions to a class of linear non-autonomous neutral delay differential equation with proportional delays.
Abstract: This paper is concerned with the long-time behaviour of the numerical solutions to a class of linear non-autonomous neutral delay differential equation with proportional delays. Our purpose is to give some asymptotic estimates of the θ-methods with constant stepsize discretization and formulate their upper bounds. Asymptotic estimate not only describes more accurate than asymptotic stability, but also gives an upper bound estimate of the solution for the long-time behaviour. We also compare the known results and show that our formulae improve and generalize these results. Some numerical examples are given in the end of this paper to confirm the theoretical results.

4 citations


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