Method of Difference Potentials and Its Applications
The method of difference potentials (MDP) was proposed in [1]-[8] and sig nificantly developed in [9]-[101] and some other works. The present book describes the current state of the art in the method of difference potentials and is a revised and essentia
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Springer-Verlag Berlin Heidelberg GmbH
Viktor S. Ryaben'kii
Method of Difference Potentials and Its
Applications
,
Springer
viktor S. Ryaben'kii Keldysh Institute for Applied Mathematics RussianAcademy of Sciences 4 Miusskaya Square 125047 Moscow, Russia e-mail: [email protected] Translator: Nikolai K. Kulman Moscow State Institute of Electronics and Mathematics Trekhsvyatitel'skii per., 3/12 109028 Moscow, Russia e-mail: [email protected] Title of Russian edition: Metod raznostnykh potentsialov i ego primeneniya Fizmatlit,Moscow, 2.001 Mathematics Subject Classification (2.000): 45-02., 31-02., 31C2.0, 65-02., 65N99
Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Rjabenkii, Viktor S.: Method of difference potentials and its applications I Viktor S. Ryaben'kii. [TransI.: Nikolai K. Kulman.- Berlin; Heidelberg ; NewYork; Barcelona ; Hong Kong ; London ; Milan ; Paris; Tokyo: Springer,2.002. (Springer series in computational mathematics ; 30) ISBN 978-3-642-62715-6 ISBN 978-3-642-56344-7 (eBook) DOI 10.1007/978-3-642-56344-7
ISSN 0179-3632 ISBN 978-3-642-62715-6 This work is subject ta copyright. AIIrights are reserved, whether the whole ar part of the material is concemed, specifically the rights of translation, reprinting, reuse of illustrations, recitation , broadcasting, reproduction an microfilm ar in any other way.and storage in data banks. Duplicalion of this publicat ion ar parts thereof is permitted only under the provisions of the German Copyright Lawof Seplember 9. 1965.in its current version. and permission for use must alwaysbe obtained from Springer.Verlag. Violations are liable for prosecution under the German Copyright Law. hup:llwww.springer.de Q Springer-Verlag Berlin Heidelberg 2002 OriginaJly publiahed by Springer-Verlag Berlin Heidelberg New York in 2002 Softcover reprint of the hardcover 1st edition 2002
The use of general descriptive names, registered names, trademarks etc, in this publicalion does noI imply, even in the absence of a specific statement, that such names are exempl from the relevant protective laws and regulations and therefore free for general use. Cover design: design&production. Heidelberg Camera-ready copy by the authors Printed on acid-free paper
SPIN 10784258
46/3142db-543210
Dedicated to the memory of my parents Solomon Abramovich Ryaben'kii and Berta Pavlovna Ryaben'kaya
Preface to the English Edition
The method of difference potentials (MDP) was proposed in [1]-[8] and significantly developed in [9]-[101] and some other works. The present book describes the current state of the art in the method of difference potentials and is a revised and essentially supplemented version of the author's first book devoted to this method, which was published by "Nauka" in 1987 [100] . This monograph deals with the MDP apparatus and several of its applications, particularly to the following problems: 1. the numerical solution of interior and exterior boundary-value problems for systems of partial differential equations; 2. th
