| 書目名稱 | Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations | | 編輯 | Mitsuhiro T. Nakao,Michael Plum,Yoshitaka Watanabe | | 視頻video | http://file.papertrans.cn/670/669251/669251.mp4 | | 概述 | Is the first published monograph on computer-assisted proofs.Presents pioneering work on the numerical verification method of solution for partial differential equations.Provides verification techniqu | | 叢書名稱 | Springer Series in Computational Mathematics | | 圖書封面 |  | | 描述 | In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information..The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -?u=f(x,u,?u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense..In this monograph, the authors give a detailed description of the verified computations and computer-assisted proo | | 出版日期 | Book 2019 | | 關(guān)鍵詞 | Numerical verification methods for nonlinear problems; Computer-assisted proofs in analysis; Nonlinear | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-13-7669-6 | | isbn_softcover | 978-981-13-7671-9 | | isbn_ebook | 978-981-13-7669-6Series ISSN 0179-3632 Series E-ISSN 2198-3712 | | issn_series | 0179-3632 | | copyright | Springer Nature Singapore Pte Ltd. 2019 |
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