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, the authors derived expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations, taking into account the effect of the roots of the characteristic equation on the representation of solutions.
Abstract: We derive expansions with exact asymptotic expressions for the remainders for solutions of multi-dimensional renewal equations. The effect of the roots of the characteristic equation on the asymptotic representation of solutions is taken into account. The resulting formulae are used to investigate the asymptotic behaviour of the average number of particles in age-dependent branching processes having several types of particles.
2 citations
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TL;DR: In this paper, an algorithm for the approximate solution (in the asymptotic sense) of a singularly perturbed linear time-optimal control problem is proposed, and a computational procedure is outlined, which permits the use of the resulting approximation for.
2 citations
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TL;DR: Asymptotic behavior for solutions of neutral difference equations dealing with mechanical vibration problems and other related topics, and some theorems have been obtained, are studied in this article, where the authors consider the problem of finding the optimal solution of a neutral difference equation.
Abstract: Asymptotic behavior is studied for solutions of neutral difference equations dealing with mechanical vibration problems and other related topics, and some theorems have been obtained.
2 citations
23 Mar 2000
TL;DR: In this paper, in two dimensions, uniform asymptotic expansions of the Schwartz kernels of these operators are derived and a uniform ascyptotic expansion of the one-way propagator appearing in the series is derived.
Abstract: The Bremmer coupling series solution of the wave equation, in generally inhomogeneous media, requires the introduction of pseudodifferential operators. In this paper, in two dimensions, uniform asymptotic expansions of the Schwartz kernels of these operators are derived. Also, we derive a uniform asymptotic expansion of the one-way propagator appearing in the series. We focus on designing closed-form representations, valid in the high-frequency limit, taking into account critical scattering-angle phenomena. Our expansion is not limited by propagation angle. In principle, the uniform asymptotic expansion of a kernel follows by matching its asymptotic behaviors away from and near its diagonal. The Bremmer series solver consists of three steps: directional decomposition into up- and downgoing waves, one-way propagation, and interaction of the counter-propagating constituents. Each of these steps is represented here by a kernel for which a uniform asymptotic expansion is found. The associated algorithm provid...
2 citations