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 paper, the authors studied the asymptotic behavior of Navier-Stokes equations linearized around the rest state as viscostiy " approaches zero and obtained convergence results valid up to the boundary.
Abstract: We continue our study of the asymptotic behavior of the Navier-Stokes equations linearized around the rest state as viscostiy " approaches zero. We study the convergence as "! 0 to the inviscid type equations. Suitable correctors are obtained which resolve the boundary layer and we obtain convergence results valid up to the boundary. Explicit asymptotic expansion formulas are given which display the boundary layer phenomena. We improve our previous by treating here the general smooth bounded domain in R 2 instead of two-dimensional channels. Curvilinear coordinates are used to resolve the complex geometry.
25 citations
01 Jan 1985
TL;DR: In this article, the asymptotic behavior of solutions of Volterra integrodifferential equations of the form x'(t) = A (t)x(t), + J K(t, s),x(s) ds + F(t).
Abstract: The asymptotic behavior of solutions of Volterra integrodifferential equations of the form x'(t) = A(t)x(t) + J K(t, s)x(s) ds + F(t) is discussed in which A is not necessarily a stable matrix. An equivalent equation which involves an arbitrary function is derived and a proper choice of this function would pave a way for the new coefficient matrix B (corresponding A) to be stable.
25 citations
TL;DR: In this paper, the authors compare optimal homotopy asymptotic method and perturbation-iteration method to solve random nonlinear differential equations, and give some numerical examples to prove these claims.
Abstract: In this paper, we compare optimal homotopy asymptotic method and perturbation-iteration method to solve random nonlinear differential equations. Both of these methods are known to be new and very powerful for solving differential equations. We give some numerical examples to prove these claims. These illustrations are also used to check the convergence of the proposed methods.
25 citations
TL;DR: In this paper, an extension of the first-order analysis is presented, in which the expansion parameter is the eigenvalue and matching of both amplitude and phase of functions are required.
25 citations
TL;DR: In this article, the authors present a systematic study of localized asymptotic solutions of the one-dimensional wave equation with variable velocity, which can be used in more complicated cases such as inhomogeneous wave equations, the linear surge problem, the small dispersion case, etc.
Abstract: We present a systematic study of the construction of localized asymptotic solutions of the one-dimensional wave equation with variable velocity. In part I, we discuss the solution of the Cauchy problem with localized initial data and zero right-hand side in detail. Our aim is to give a description of various representations of the solution, their geometric interpretation, computer visualization, and illustration of various general approaches (such as the WKB and Whitham methods) concerning asymptotic expansions. We discuss ideas that can be used in more complicated cases (and will be considered in subsequent parts of this paper) such as inhomogeneous wave equations, the linear surge problem, the small dispersion case, etc. and can eventually be generalized to the 2-(and n-) dimensional cases.
25 citations