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: In this article, an asymptotic expansion in terms of the amplitude and phase of the solution is developed for determining approximate solutions to a class of differential equations characterized by resonance phenomena where resonance phenomena (arising, for example, when ƒ(x, [xdot], t) = ǫ cosω0 t) may be neglected.
Abstract: A method is presented for determining approximate solutions to a class of differential equations characterized by: where resonance phenomena (arising, for example, when ƒ(x, [xdot], t) = x cosω0 t) may be neglected. The approximation is developed from an asymptotic expansion in terms of the amplitude and phase of the solution. Three examples are considered in illustration of the application of the approximation technique, and using an integral error function, solution error is shown graphically for these examples in terms of equation parameters. An expression for the approximate solution is derived which makes it possible to determine solution accuracy for any function f(x, x˙, t) once the approximate amplitude envelope and phase relationships have been derived. Graphical solutions demonstrate the accuracy which can be maintained even up to relatively large values of the parameter µ.
24 citations
01 Jan 2008
TL;DR: In this paper, the authors investigate a model of nonlinearly perturbed continuous-time renewal equation, where some characteristics of the renewal equation are assumed to have non-polynomial perturbations.
Abstract: In this thesis we investigate a model of nonlinearly perturbed continuous-time renewal equation. Some characteristics of the renewal equation are assumed to have non-polynomial perturbations, more specifically they can be expanded with respect to a non-polynomial asymptotic scale. The main result of the present study is exponential asymptotic expansions for the solution of the perturbed renewal equation. These asymptotic results are also applied to various applied probability models like perturbed risk processes, perturbed M/G/1 queues and perturbed dam/storage processes. The thesis is based on five papers where the model described above is successively studied.
24 citations
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TL;DR: In this paper, the perturbation expansions are derived by a technique which does not assume that convergent expansions exist, and criteria are developed to determine if a finite number of terms underestimates or overestimates the exact result for sufficiently small values of the coupling constant.
Abstract: The perturbation expansions are derived by a technique which does not assume that convergent expansions exist. The theory is shown to be asymptotic, and criteria are developed to determine if a finite number of terms underestimates or overestimates the exact result for sufficiently small values of the coupling constant.
24 citations
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TL;DR: In this article, the Nielsen fixed point theory is used to study singularly perturbed higher order ODEs depending on parameters and lower bounds of the number of parameters for which those equations possess a solution.
24 citations