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 article, the authors considered the problem of finding the asymptotic stability of solutions of (1.1) when the kernel a(t) is known to have a specific (asymptotically stable) representation.
Abstract: and a(t) * a(O+), then the solution u(t) of (1.1) satisfies (1.2). In this paper, we are not concerned with sufficient conditions for the asymptotic stability of (1.1) but rather with the rate of decay of solutions of (1.1) when it is known that the equation is asymptotically stable. Thus, when the kernel a(t) is known to have a specific asymptotic representation, one seeks for asymptotic representation of the solution of (1.1). This approach has been investigated in a recent paper of
12 citations
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15 Nov 2010
12 citations
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TL;DR: In this paper, the asymptotic properties of a class of nonlinear boundary value problems are studied, and very simple approximate analytic solutions are obtained, and their accuracy is illustrated by showing their good agreement with the exact numerical solution of the problem.
Abstract: The asymptotic properties of a class of nonlinear boundary‐value problems are studied. For large values of a parameter, the differential equation is of the singular‐perturbation type, and its solution is constructed by means of matched asymptotic expansions. In two special cases, very simple approximate analytic solutions are obtained, and their accuracy is illustrated by showing their good agreement with the exact numerical solution of the problem.
12 citations
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12 citations
01 Jan 1990
12 citations