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, an asymptotic expansion is proposed for the construction of estimates with a prescribed influence function in parametric and semiparametric models, where the influence function is defined in terms of a fixed influence function.
7 citations
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7 citations
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TL;DR: The equivalent, second equivalent and (simply) modified equations for the implicit midpoint rule are shown to be asymptotically equivalent in the sense that anAsymptotic analysis of these equations with the time step size as small parameter yields exactly the same results; for linear problems with constant coefficients, they are also equivalent to the original finite difference scheme.
7 citations
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TL;DR: In this paper, the eigenvalues for the convolution operator of u where u is between 0 and 1 were found for the CNN operator with respect to the parameters of u.
Abstract: The eigenvalues are found for the convolution operator of u where u is between 0 and 1.(AIP)
7 citations
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TL;DR: In this article, the authors compared the results obtained from the exact solution, from those found by Reiss and from the matched asymptotic expansion solution developed here, show that the last is far more accurate than the second.
Abstract: Traditional singular perturbation methods are employed to develop a solution to a differential equation considered by Reiss [SIAM J. Appl. Math., 39 (1980), pp. 440–455] which models an elementary chemical process. The results are compared with those found by Reiss, who used a novel asymptotic method to construct solutions which exhibit rapid transient behavior. It is shown that Reiss’ jump solution corresponds to the asymptotic (large time) representation of the more complete solution found from a formal matched asymptotic expansion procedure. A comparison of results in the rapid transition region obtained from the exact solution, from those found by Reiss and from the matched asymptotic expansion solution developed here, show that the last is far more accurate than the second.
7 citations