Topic
Method of matched asymptotic expansions
About: Method of matched asymptotic expansions is a research topic. Over the lifetime, 4233 publications have been published within this topic receiving 73311 citations.
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TL;DR: In this article, a mixed boundary-value problem for the Poisson equation in a plane two-level junction is considered, where the thin rods from each level are e-periodically alternated.
Abstract: We consider a mixed boundary-value problem for the Poisson equation in a plane two-level junction Ωe, which is the union of a domain Ω0 and a large number 2N of thin rods with variable thickness of order . The thin rods are divided into two levels depending on their length. In addition, the thin rods from each level are e-periodically alternated. The Robin conditions are given on the lateral boundaries of the thin rods. Using the method of matched asymptotic expansions, we construct the asymptotic approximation for the solution as e → 0 and prove the corresponding estimates in the Sobolev space H1(Ωe).
40 citations
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40 citations
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TL;DR: In this article, asymptotic expansions for the exponentially small splitting of separatrices of area preserving maps combining analytical and numerical points of view are studied using high-precision arithmetic, which involves up to several thousands of decimal digits.
Abstract: We study asymptotic expansions for the exponentially small splitting of separatrices of area preserving maps combining analytical and numerical points of view. Using analytic information, we conjecture the basis of functions of an asymptotic expansion and then extract actual values of the coefficients of the asymptotic series numerically. The computations are performed with high-precision arithmetic, which involves up to several thousands of decimal digits. This approach allows us to obtain information which is usually considered to be out of reach of numerical methods. In particular, we use our results to test that the asymptotic series are Gevrey-1 and to study positions and types of singularities of their Borel transform. Our examples are based on generalisations of the standard and Henon maps.
40 citations
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TL;DR: In this article, an asymptotic theory for dynamic analysis of doubly curved laminated shells is formulated within the framework of three-dimensional elasticity, where multiple time scales are introduced in the formulation so that the secular terms can be eliminated in obtaining a uniform expansion leading to valid asymptic solutions.
39 citations