Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
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, compu
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Mitsuhiro T. Nakao Michael Plum Yoshitaka Watanabe
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
Springer Series in Computational Mathematics Volume 53
Series Editors Randolph E. Bank, Department of Mathematics, University of California, San Diego, La Jolla, CA, USA Ronald L. Graham, Department of Computer Science & Engineering, University of California, San Diego, La Jolla, CA, USA Wolfgang Hackbusch, Max-Planck-Institut für Mathematik in den Naturwissenschaften, Leipzig, Germany Josef Stoer, Institut für Mathematik, University of Würzburg, Würzburg, Germany Richard S. Varga, Kent State University, Kent, OH, USA Harry Yserentant, Institut für Mathematik, Technische Universität Berlin, Berlin, Germany
This is basically a numerical analysis series in which high-level monographs are published. We develop this series aiming at having more publications in it which are closer to applications. There are several volumes in the series which are linked to some mathematical software. This is a list of all titles published in this series.
More information about this series at http://www.springer.com/series/797
Mitsuhiro T. Nakao • Michael Plum Yoshitaka Watanabe
Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
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Mitsuhiro T. Nakao Faculty of Mathematics Kyushu University Fukuoka, Japan
Michael Plum Faculty of Mathematics Karlsruhe Institute of Technology Karlsruhe, Germany
Yoshitaka Watanabe Research Institute for Information Technology Kyushu University Fukuoka, Japan
ISSN 0179-3632 ISSN 2198-3712 (electronic) Springer Series in Computational Mathematics ISBN 978-981-13-7668-9 ISBN 978-981-13-7669-6 (eBook) https://doi.org/10.1007/978-981-13-7669-6 © Springer Nature Singapore Pte Ltd. 2019 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint
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