scispace - formally typeset
Search or ask a question
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.


Papers
More filters
Journal ArticleDOI
TL;DR: Using Heaviside's exponential series, a power series solution of the differential equation is split into formal solutions with known asymptotic expansions as discussed by the authors, where the expansion is defined by a set of constants.
Abstract: Using Heaviside’s exponential series, a power series solution of the differential equation is split into formal solutions with known asymptotic expansions.

25 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that lifting-line theory can be easily derived by applying the method of asymptotic expansions to the integral equation given by lifting-surface theory.
Abstract: The purpose of the present paper is to show that lifting-line theory can be easily derived by applying the method of asymptotic expansions to the integral equation given by lifting-surface theory, in contrast to Van Dyke's paper [1] in which lifting-line theory is derived by applying the method of matched asymptotic expansions to a partial differential equation. Moreover, the present paper shows that there is an error in Van Dyke's paper about the third-order inner approximation, and the corrected formula about the circulation is obtained.

25 citations

Journal ArticleDOI
TL;DR: In this article, the traveling-wave Fisher equation was studied and the authors showed that the solution will have a corner layer (a shock in the derivative) as the diffusion coefficient approaches a step function, and the corner layer at z = 0 is matched to an outer solution for z 0 to produce a complete solution.
Abstract: We examine traveling-wave solutions for a generalized nonlinear-diffusion Fisher equation studied by Hayes [J. Math. Biol. 29, 531–537 (1991)]. The density-dependent diffusion coefficient used is motivated by certain polymer diffusion and population dispersal problems. Approximate solutions are constructed using asymptotic expansions. We find that the solution will have a corner layer (a shock in the derivative) as the diffusion coefficient approaches a step function. The corner layer at z = 0 is matched to an outer solution for z 0 to produce a complete solution. We show that this model also admits a new class of nonphysical solutions and obtain conditions that restrict the set of valid traveling-wave solutions.

25 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that interfacial solitary structures generated by a bistable chemical reaction can be stabilized by Marangoni flow preventing the spread of a dynamically favorable state with a higher surface tension.
Abstract: It is shown that interfacial solitary structures (spots) generated by a bistable chemical reaction can be stabilized by Marangoni flow preventing the spread of a dynamically favorable state with a higher surface tension. The solutions are constructed using the method of matched asymptotic expansions to resolve the singularity at a sharp interface between the alternative states, and to compute the self-induced flow velocity advecting the domain boundary. {copyright} {ital 1997} {ital The American Physical Society}

25 citations


Network Information
Related Topics (5)
Partial differential equation
70.8K papers, 1.6M citations
90% related
Differential equation
88K papers, 2M citations
89% related
Boundary value problem
145.3K papers, 2.7M citations
86% related
Bounded function
77.2K papers, 1.3M citations
84% related
Nonlinear system
208.1K papers, 4M citations
83% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835