Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: This study focuses on the difference equations representing the probabilityvector, and aims at deriving matched asymptotic expansions of the solutions of singularly perturbed discrete-time Markov chains.
Abstract: Originating from a wide range of applications in optimization and control of large-scale systems (such as telecommunications, queueing networks, and manufacturing systems), this work is devoted to a class of singularly perturbed discrete-time Markov chains. The states of the Markov chain are naturally decomposable into recurrent and transient classes such that within each class the interactions are strong and among different classes the interactions are weak. Our study focuses on the difference equations representing the probabilityvector, and aims at deriving matched asymptotic expansions of the solutions. Justification and error analysis are also provided. Both time-homogeneous and time-inhomogeneous models are examined.
41 citations
TL;DR: In this article, a new method for representing the remainder and coefficients in Airy-type expansions of integrals is given, where quantities are written in terms of Cauchy-type integrals and are natural generalizations of integral representations of Taylor coefficients and remainders of analytic functions.
Abstract: A new method for representing the remainder and coefficients in Airy-type expansions of integrals is given. The quantities are written in terms of Cauchy-type integrals and are natural generalizations of integral representations of Taylor coefficients and remainders of analytic functions. The new approach gives a general method for extending the domain of the saddle-point parameter to unbounded domains. As a side result the conditions under which the Airy-type asymptotic expansion has a double asymptotic property become clear. An example relating to Laguerre polynomials is worked out in detail. How to apply the method to other types of uniform expansions, for example, to an expansion with Bessel functions as approximants, is explained. In this case the domain of validity can be extended to unbounded domains and the double asymptotic property can be established as well.
41 citations
TL;DR: In this paper, the Laplace transform technique is used to solve the problem of generalized thermoelasticity with one relaxation time and the inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time.
Abstract: In this work, we consider the one-dimensional problem for an infinitely long hollow cylinder in the context of the theory of generalized thermoelasticity with one relaxation time. The Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time. The temperature, displacement, and stress are computed and represented graphically.
40 citations
01 Apr 2007
40 citations
TL;DR: In this article, a complete procedure is given to determine the outer and inner expansions of a singularly perturbed boundary value problem in $\mathbb{R}^n $. The validity of such expansions is deduced from a gene...
Abstract: A complete procedure is given to determine the outer and inner expansions of a singularly perturbed boundary value problem in $\mathbb{R}^n $. The validity of such expansions is deduced from a gene...
40 citations