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 studied the asymptotic behavior of solutions for a class of nonlinear difference equations and gave the results about the solutions of the equations convergent to a constant.
Abstract: In this paper, we study the asymptotic behavior of solutions for a class of nonlinear difference equations and give the results about the solutions of the equations convergent to a constant. Our results generalize all conclusions obtained in [1].
5 citations
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TL;DR: For a simple model of a linear kinetic equation, the exact solution is expanded in terms of a small parameter whose presence makes the equation, singularly perturbed as discussed by the authors, and it is shown that the compressed method, which is related to the Chapman-Enskog asymptotic procedure, is the most accurate.
Abstract: For a simple model of a linear kinetic equation the exact solution is expanded in terms of a small parameter whose presence makes the equation, singularly perturbed. Various asymptotic expansion methods are analyzed and it is shown that the compressed method, which is related to the Chapman-Enskog asymptotic procedure, is the most accurate. This holds when the technique of time rescaling is applied to overcome the difficulties with the application of the standard asymptotic procedure.
5 citations
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5 citations
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TL;DR: In this paper, it is proved rigorously that the leading term in the outer asymptotic expansion of the time dependent solution describing relaxation oscillations of the Van der Pol equation is correct.
Abstract: It is proved rigorously that the leading term in the outer asymptotic expansion of the time dependent solution describing relaxation oscillations of the Van der Pol equation is correct. This is accomplished by constructing rigorous estimates of the difference between the exact solution and the outer asymptotic solution as constructed by J. D. Cole. These estimates are both rigorous and numerically computable.
5 citations