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: The Asymptotic stability of a class of linear difference equations has been studied in this paper, where the authors show that linear difference equality is stable in terms of the number of differences.
Abstract: (1996). On the Asymptotic Stability of a Class of Linear Difference Equations. Mathematics Magazine: Vol. 69, No. 1, pp. 34-43.
44 citations
TL;DR: A computational method is suggested in which exponentially fitted difference schemes are combined with classical numerical methods to obtain numerical solution of singularly perturbed turning point problems for second order ordinary differential equations exhibiting twin boundary layers.
43 citations
01 Jan 2005
TL;DR: In this paper, a stability theory for spatially periodic patterns on R was developed for a class of singularly perturbed reaction-diffusion equations that can be represented by the generalized Gierer-Meinhardt equations as "normal form".
Abstract: In this paper we develop a stability theory for spatially periodic patterns on R. Our approach is valid for a class of singularly perturbed reaction-diffusion equations that can be represented by the generalized Gierer-Meinhardt equations as 'normal form'. These equations exhibit a large variety of spatially periodic patterns. We construct an Evans function
43 citations
TL;DR: In this article, a constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+).
Abstract: A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.
43 citations
TL;DR: In this paper, a conditional limit theorem and conditional asymptotic expansions are considered based on the Malliavin calculus, and the problem of lifting limit theorems to their conditional counterparts is treated.
43 citations