Two-Step Multidimensional ERKN Methods
In Chap. 5, multidimensional two-step extended Runge–Kutta–Nyström-type (TSERKN) methods are developed for solving the oscillatory second-order system y″+My=f(x,y), where M∈ℝ d×d is a symmetric positive semi-definite matrix that implicitly contains the fr
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Xinyuan Wu r Xiong You r Bin Wang
Structure-Preserving Algorithms for Oscillatory Differential Equations
Xinyuan Wu Nanjing University Nanjing, China
Xiong You Nanjing Agricultural University Nanjing, China
Bin Wang Nanjing University Nanjing, China
ISBN 978-3-642-35337-6 ISBN 978-3-642-35338-3 (eBook) DOI 10.1007/978-3-642-35338-3 Springer Heidelberg New York Dordrecht London Jointly published with Science Press Beijing ISBN: 978-7-03-035520-1 Science Press Beijing Library of Congress Control Number: 2013931848 © Science Press Beijing and Springer-Verlag Berlin Heidelberg 2013 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Effective numerical solution of differential equations, although as old as differential equations themselves, has been a great challenge to numerical analysts, scientists and engineers for centuries. In recent decades, it has been universally acknowledged that differential equations arising in science and engineering often have certain structures that require preservation by the numerical integrators. Beginning with the symplectic integration of R. de Vogelaere (1956), R.D. Ruth (1983), Feng Kang (1985), J.M. Sanz-Serna (1988), E. Hairer (1994) and others, structure-preserving computation, or geometric numerical integration, ha
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