Topic
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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TL;DR: In this paper, existence theorems and asymptotic formulas for the solutions of a class of delay-differential equations with time-state dependent lag have been proved and shown to exist.
15 citations
TL;DR: In this article, the authors derive and justify two models for bending-stretching of a viscoelastic rod by using the asymptotic expansion method, and derive a model for bending and stretching of the rod.
15 citations
01 Jan 2003
TL;DR: In this article, an asymptotic representation for a fundamental solution matrix for scalar linear dynamic systems on time scales is given, which is a generalization of the usual exponential function.
Abstract: We consider linear dynamic systems on time scales, which contain as special cases linear differential systems, difference systems, or other dynamic systems. We give an asymptotic representation for a fundamental solution matrix that reduces the study of systems in the sense of asymptotic behavior to the study of scalar dynamic equations. In order to understand the asymptotic behavior of solutions of scalar linear dynamic equations on time scales, we also investigate the behavior of solutions of the simplest types of such scalar equations, which are natural generalizations of the usual exponential function.
15 citations
TL;DR: A Finite Element Method implementation for the asymptotic partial decomposition is considered and the relation with the “mixed formulation” is discussed.
Abstract: We consider a Finite Element Method (F.E.M.) implementation for the asymptotic partial decomposition. The advantage of this approach is an important reduction of the number of nodes. The convergence is proved for some model problems. Finally the relation with the “mixed formulation” is discussed.
15 citations
01 Aug 1992
TL;DR: Based on previous work on asymptotic expansions, this work gives an algorithm which computes Hardy-field solutions of equations f(y) = x, with f belonging to a large class of functions.
Abstract: We study the automatic computation of asymptotic expansions of functional inverses. Based on previous work on asymptotic expansions, we give an algorithm which computes Hardy-field solutions of equations f(y) = x, with f belonging to a large class of functions.
14 citations