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, the asymptotic estimate for large solutions of one-dimensional generalized diffusion equations with regularly varying Green functions was given for all solutions of the semigroup T_tf(x) with speed measure functions.
Abstract: We give the asymptotic estimate for large $t$ of elementary solutions of one-dimensional generalized diffusion equations with regularly varying Green functions. As a corollary we obtain the precise asymptotic behavior of the semigroup $T_tf(x)$ for all $f \in L_1(dm)$ if the speed measure function $m(x)$ is regularly varying as $x \rightarrow \pm \infty$.
19 citations
TL;DR: In this article, an analogue of the analytic Hamiltonian formalism in a complex phase space is presented for constructing formal asymptotic solutions of the characteristics and the transport equation.
Abstract: In this paper we give a method for constructing formal asymptotic solutions. This method uses in some sense "approximate solutions" of the equation of the characteristics and the transport equation. The construction of approximate solutions is brought abount by means of an analogue of the analytic Hamiltonian formalism in a complex phase space. Bibliography: 19 items.
19 citations
TL;DR: In this article, an exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm, with respect to the perturbation parameter.
Abstract: This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.
19 citations
TL;DR: In this article, the second terms of the asymptotic expansions of Toth's formulae are extended by specifying the second term of the first terms of their expansions.
Abstract: L. Fejes Toth gave asymptotic formulae as n → ∞ for the distance between a smooth convex disc and its best approximating inscribed or circumscribed polygons with at most n vertices, where the distance is in the sense of the symmetric difference metric. In this paper these formulae are extended by specifying the second terms of the asymptotic expansions. Tools are from affine differential geometry.
19 citations
TL;DR: The closure problem for combustion waves arises when applying the method of matched asymptotic expansions for large activation energy to many nonsteady combustion problems.
Abstract: The closure problem for combustion waves arises when applying the method of matched asymptotic expansions for large activation energy to many nonsteady combustion problems. The exponential nature of the dependence of the reaction rate on temperature and the large coefficient (activation energy) in the exponent lead to the first order correction for temperature appearing in the equations at leading order. Equations describing the first order correction involve the second order correction, and so on. These terms can be scaled away for steady solutions, but when considering nonsteady propagation, they remain for any constant scaling of temperature. The closure problem refers to the fact that the equations must be solved at all orders before the leading order solution can be determined. One traditional approach to alleviate the problem is to truncate the series. While sacrificing the distinction between scales of temperature variation ahead of and behind the flame, these methods allow the replacement of the d...
19 citations