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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 results of numerical examples show that the present method for solving singularly perturbed turning point problems exhibiting an interior layer can provide very accurate approximate solutions.

111 citations

Journal ArticleDOI
TL;DR: In this article, a mathematical discussion of the exchange processes, of heat or of matter (as in ion exchange or adsorption), that arise when a fluid flows through the pores or voids along a column containing matter in the solid state is presented.
Abstract: The paper is intended as a contribution to the mathematical discussion of the exchange processes, of heat or of matter (as in ion exchange or adsorption), that arise when a fluid flows through the pores or voids along a column containing matter in the solid state. The exchange is taken to be governed by a linear or bilinear or Langmuir-type kinetic exchange equation. The matters dealt with include the solution of the exchange and conservation equations for any initial conditions, mathematical properties of and asymptotic expansions for the functions arising, and the appearance of the functions in the solutions of other physical problems. The discussion of the mathematical properties of the functions and their asymptotic expansions is needed to establish the relationship between solutions on the equilibrium theory and those on the kinetic theory, and to find closer approximations to the kinetic-theory solutions.

110 citations

Journal ArticleDOI
TL;DR: In this article, the singular perturbation technique was used to obtain an approximate solution to the aircraft minimum time-to-climb problem, which is the same as the one we consider in this paper.
Abstract: Application of singular perturbation techniques to trajectory optimization problems of flight mechanics is discussed. The method of matched asymptotic expansions is used to obtain an approximate solution to the aircraft minimum time-to-climb problem. Outer, boundary-layer, and composite solutions are obtained to zeroth and first orders. A stability criterion is derived for the zeroth-order boundary-layer solutions (the theory requires a form of boundary-layer stability). A numerical example is considered for which it is shown that the stability criterion is satisfied and a useful numerical solution is obtained. The zeroth-order solution proves to be a poor approximation, but the first-order solution gives a good approximation for both the trajectory and the minimum time-to-climb. The computational cost of the singular perturbation solution is considerably less than that of a steepest descent solution. Thus singular perturbation methods appear to be promising for the solution of optimal control problems.

110 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered an ordinary differential equation of quite general form and showed how to find the following near a finite or infinite value of the independent variable by using algorithms of power geometry.
Abstract: An ordinary differential equation of quite general form is considered. It is shown how to find the following near a finite or infinite value of the independent variable by using algorithms of power geometry: (i) all power-law asymptotic expressions for solutions of the equation; (ii) all power-logarithmic expansions of solutions with power-law asymptotics; (iii) all non-power-law (exponential or logarithmic) asymptotic expressions for solutions of the equation; (iv) certain exponentially small additional terms for a power-logarithmic expansion of a solution that correspond to exponentially close solutions. Along with the theory and algorithms, examples are presented of calculations of the above objects for one and the same equation. The main attention is paid to explanations of algorithms for these calculations.

108 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202321
202244
202110
202023
201913
201835