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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01 Sep 2012
TL;DR: In this paper, a numerical integration method to solve singularly perturbed delay differential equations is presented, in which linear interpolation is used to get three term recurrence relation which is solved easily by discrete invariant imbedding algorithm.
Abstract: In this paper, we present a numerical integration method to solve singularly perturbed delay differential equations. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the numerical integration. Then, linear interpolation is used to get three term recurrence relation which is solved easily by discrete invariant imbedding algorithm. The method is demonstrated by implementing several model examples by taking various values for the delay parameter and perturbation parameter.
19 citations
TL;DR: It is shown that the convergence of block-diagonalization of a singularly perturbed system is ensured under restrictions which are less restrictive than the case of previously suggested methods.
Abstract: Block-diagonalization of a singularly perturbed system requires the solution of the Riccati equation and the Lyapunov equation. A new approach is suggested for both equations, using Taylor expansions. The convergence is studied in detail; it is shown that it is ensured under restrictions which are less restrictive than the case of previously suggested methods. >
19 citations
TL;DR: In this paper, the periodic solution of a Volterra-lotka system is considered as a relaxation oscillation, and four local expansions are constructed from the implicitly given solution.
Abstract: The periodic solution of a Volterra-Lotka system is considered as a relaxation oscillation. With perturbation techniques, four local expansions are constructed from the implicitly given solution. Integration over the four regions leads to an asymptotic formula for the period.
19 citations
TL;DR: In this paper, a comprehensive analytical solution for fuel cell transport is presented, and the analytical results are used to investigate several aspects of transport phenomena and their substantial role in PEM fuel cell operation.
19 citations
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TL;DR: In this paper, the problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated.
Abstract: The problem of extrapolating asymptotic perturbation-theory expansions in powers of a small variable to large values of the variable tending to infinity is investigated. The analysis is based on self-similar approximation theory. Several types of self-similar approximants are considered and their use in different problems of applied mathematics is illustrated. Self-similar approximants are shown to constitute a powerful tool for extrapolating asymptotic expansions of different natures.
19 citations