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 Dirichlet problem for the Poisson equation is considered in a nonperiodic framelike domain that consists of thin short strips or cylinders, and an estimate for the difference between the exact solution and the asymptotic one is obtained.
Abstract: In this paper, the Dirichlet problem for the Poisson equation is considered in a nonperiodic framelike domain that consists of thin short strips or cylinders. We construct a complete asymptotic expansion for the solution. We obtain an estimate for the difference between the exact solution and the asymptotic one. Bibliography: 9 titles.
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TL;DR: This special issue consists mainly of a collection of presentations at the 3rd International Symposium on Nonlinear Dynamics, Shanghai, China, conveying a strong, reliable, efficient, and promising development of various asymptotic methods.
Abstract: where the unknown constants a, b and ω can be determined by substituting (4) into (1). For practical problems, we can not obtain such a good initial condition like Eq. (3), sometimes the measured initial/boundary conditions have to be expressed in approximate forms, and sometimes only some point values on boundaries can be measured, we call these problems as approximate initial/boundary conditions and point boundary conditions, respectively, such problems can not be solved exactly but asymptotically. Asymptotical approach to nonlinear equations, fractional differential equations, and problemswith approximate initial/boundary conditions or point boundary conditions is the next frontier towards nonlinear science [1]. The oldest asymptotic method is the Ying Buzu Shu, which appeared in an ancient Chinese classic called Jiu Zhang Suan Shu (Nine Chapters on the Art of Mathematics), for solving algebraic equations, and the method has been widely used to solve nonlinear differential equations, especially nonlinear oscillators and with great success as shown in this special issue by Hui-Li Zhang and Zhong-fu Ren, respectively. In Ref. [2] many asymptotic methods were systematically reviewed, and their potential applications were outlined. This special issue consists mainly of a collection of presentations at the 3rd International Symposium on Nonlinear Dynamics, September 25–28, 2010, Shanghai, China, conveying a strong, reliable, efficient, and promising development of various asymptotic methods. Included herein is a collection of original refereed research papers by well-established researchers in the field of nonlinear science. We hope that these papers will prove to be a timely and valuable reference for researchers in this area. In this special issue, various asymptotic methods (e.g. Hamiltonian approach, Adomian method, variational iteration method, homotopy perturbation method, exp-function method, differential transformation method and ancient Chinese algorithm) for real-life nonlinear problems are given and can be used as paradigms for many other applications. The aim of this special issue is to bring to the fore themany new and exciting applications of the asymptoticmethods, thereby capturing both the interest and imagination of the wider communities in various fields. Finally I would like to express my appreciation to the editor-in-chief of Computers & Mathematics with Applications, Prof. Ervin Y. Rodin, and all reviewers who took the time to review articles in a very short time.
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