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Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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01 Jan 1971
2 citations
TL;DR: In this article, the authors present two algorithms for constructing canonical factorizations of disconjugate operators starting from a basis of their kernel, which form a Chebyshev asymptotic scale at an endpoint.
Abstract: This part II-C of our work completes the factorizational theory of asymptotic expansions in the real domain. Here we present two algorithms for constructing canonical factorizations of a disconjugate operator starting from a basis of its kernel which forms a Chebyshev asymptotic scale at an endpoint. These algorithms arise quite naturally in our asymptotic context and prove very simple in special cases and/or for scales with a small numbers of terms. All the results in the three Parts of this work are well illustrated by a class of asymptotic scales featuring interesting properties. Examples and counterexamples complete the exposition.
2 citations
TL;DR: In this paper, the authors considered the asymptotic evaluation of an acoustic field propagating on the surface of a piezoelectric material covered with conductors and constructed uniform expansions based on the Bleistein-Handelsman theory.
2 citations
27 Apr 2016
TL;DR: In this article, a generalized method of boundary functions was proposed for constructing complete asymptotic expansions of the solutions to the Dirichlet problem for bisingular perturbed linear inhomogeneous second-order elliptic equations with two independent variables in the ring.
Abstract: The Dirichlet problem for elliptic equations with a small parameter in the highest derivatives takes a unique place in mathematics. In general case it is impossible to build explicit solution to these problems, which is why the researchers apply different asymptotic methods. The aim of the research is to develop the asymptotic method of boundary functions for constructing complete asymptotic expansions of the solutions to such problems. The proposed generalized method of boundary functions differs from the matching method in the fact that the growing features of the outer expansion are actually removed from it and with the help of the auxiliary asymptotic series are fully included in the internal expansions, and differs from the classical method of boundary functions in the fact that the boundary functions decay in power-mode nature and not exponentially. Using the proposed method, a complete asymptotic expansion of the solution to the Dirichlet problem for bisingular perturbed linear inhomogeneous second-order elliptic equations with two independent variables in the ring with quadratic growth on the boundary is built. A built asymptotic series corresponds to the Puiseux series. The basic term of the asymptotic expansion of the solution has a negative fractional degree of the small parameter, which is typical for bisingular perturbed equations, or equations with turning points. The built expansion is justified by the maximum principle
2 citations