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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17 citations
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TL;DR: In this article, the authors considered stationary solutions with internal transition layers (contrast structures) for a singularly perturbed elliptic equation that is referred to in applications as the stationary reaction-diffusion-advection equation.
Abstract: We consider stationary solutions with internal transition layers (contrast structures) for a singularly perturbed elliptic equation that is referred to in applications as the stationary reaction-diffusion-advection equation. We construct an asymptotic approximation of arbitrary-order accuracy to such solutions and prove the existence theorem. We suggest an efficient algorithm for constructing an asymptotic approximation to the localization curve of the transition layer. To justify the constructed asymptotics, we use and develop, to this class of problems, an asymptotic method of differential inequalities, which also permits one to prove the Lyapunov stability of such stationary solutions.
17 citations
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TL;DR: In this article, a methodology to obtain an approximate solution of a singularly perturbed nonlinear differential game is presented, where the outcome of the game with approximate strategies, defined as extended value, is related to the saddle-point value.
Abstract: A methodology to obtain an approximate solution of a singularly perturbed nonlinear differential game is presented. The outcome of the game with approximate strategies, defined as extended value, is related to the saddle-point value of the game. In an example of a simple pursuit-evasion game, it is shown that the proposed methodology leads to an easily implementable feedback form solution with fairly accurate results. This approach seems to be attractive for analyzing realistic air-combat models without solving a two-point boundary-value problem.
17 citations
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TL;DR: In this paper, a degenerate stable solution for a singularly perturbed scalar differential equation of second order and a scalar DDE of first or second order was proposed.
17 citations
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TL;DR: This work develops an alternative asymptotic simplex method based on Laurent series expansions that appears to be more computationally efficient and point out several possible generalizations of this method.
17 citations