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.
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TL;DR: A numerical method named as Asymptotic Initial Value Technique (AIVT) is suggested to solve the singularly perturbed boundary value problem for the second order ordinary delay differential equation with the discontinuous convection–diffusion coefficient term.
32 citations
TL;DR: In this article, a rescaling transformation bringing friction terms in the new equation is used to obtain the asymptotic solution of a one-dimensional, one-species beam.
Abstract: Rescaling transformations bringing friction terms in the new equation are used to obtain the asymptotic solution of a one-dimensional, one-species beam. It is shown that for all possible initial conditions this asymptotic solution coincides with the self-similar solution.
32 citations
TL;DR: In this article, two methods for computing the coefficients of the asymptotic series near the transition point are discussed, and auxiliary functions that can be computed more efficiently than the coefficients in the first method, and do not need the tabulation of many coefficients.
Abstract: Airy-type asymptotic representations of a class of special functions are considered from a numerical point of view. It is well known that the evaluation of the coefficients of the asymptotic series near the transition point is a difficult problem. We discuss two methods for computing the asymptotic series. One method is based on expanding the coefficients of the asymptotic series in Maclaurin series. In the second method we consider auxiliary functions that can be computed more efficiently than the coefficients in the first method, and we do not need the tabulation of many coefficients. The methods are quite general, but the paper concentrates on Bessel functions, in particular on the differential equation of the Bessel functions, which has a turning point character when order and argument of the Bessel functions are equal.
32 citations
TL;DR: In this paper, the authors considered singularly perturbed systems involving both diffusions and pure jump processes and developed asymptotic expansions for the transition density vectors via a constructive method.
Abstract: Motivated by many problems in optimization and control, this paper is concerned with singularly perturbed systems involving both diffusions and pure jump processes. Two models are treated. In the first model, the jump process changes very rapidly by comparison with the diffusion processes. In the second model, the diffusions change rapidly in comparison with the jump process. Asymptotic expansions are developed for the transition density vectors via a constructive method; justification of the asymptotic expansions and analysis of the remainders are provided.
32 citations
32 citations