scispace - formally typeset
Search or ask a question
Topic

Asymptotology

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


Papers
More filters
Journal ArticleDOI
Bixiang Wang1
TL;DR: In this article, the asymptotic behavior of solutions for parabolic non-linear evolution equations in R n is studied and the existence of the global attractor in L 2 (R n ) is established.

272 citations

Journal ArticleDOI
TL;DR: In this paper, the authors consider the case where the population value of the parameter vector is a boundary point of the feasible region and show that the asymptotic distribution of test statistic is a mixture of chi-squared distributions.
Abstract: SUMMARY The analysis of moment structural models has become an important tool of investigation in behavioural, educational and economic studies. The chi-squared largesample test is routinely employed to assess the goodness of fit of the model considered. However, in order to invoke the standard asymptotic distribution theory certain regularity conditions have to be met. Here we consider the case where the population value of the parameter vector is a boundary point of the feasible region. We show that in this case the asymptotic distribution of test statistic is a mixture of chi-squared distributions. The problem of finding the corresponding weights is discussed.

269 citations

Journal ArticleDOI
TL;DR: In this article, the authors use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a hyperasymptotic approximation.
Abstract: Singular perturbation methods, such as the method of multiple scales and the method of matched asymptotic expansions, give series in a small parameter e which are asymptotic but (usually) divergent. In this survey, we use a plethora of examples to illustrate the cause of the divergence, and explain how this knowledge can be exploited to generate a 'hyperasymptotic' approximation. This adds a second asymptotic expansion, with different scaling assumptions about the size of various terms in the problem, to achieve a minimum error much smaller than the best possible with the original asymptotic series. (This rescale-and-add process can be repeated further.) Weakly nonlocal solitary waves are used as an illustration.

261 citations


Network Information
Related Topics (5)
Stochastic partial differential equation
21.1K papers, 707.2K citations
84% related
Differential equation
88K papers, 2M citations
83% related
Numerical partial differential equations
20.1K papers, 703.7K citations
82% related
Bounded function
77.2K papers, 1.3M citations
81% related
Partial differential equation
70.8K papers, 1.6M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20231
20222
20181
201725
201626
201526