Periodic Integral and Pseudodifferential Equations with Numerical Approximation
Classical boundary integral equations arising from the potential theory and acoustics (Laplace and Helmholtz equations) are derived. Using the parametrization of the boundary these equations take a form of periodic pseudodifferential equations. A general
- PDF / 30,411,139 Bytes
- 461 Pages / 439 x 666 pts Page_size
- 98 Downloads / 246 Views
Springer Monographs in Mathematics
Springer-Verlag Berlin Heidelberg GmbH
Jukka Saranen • Gennadi Vainikko
Periodic Integral and Pseudodifferential Equations with Numerical Approximation
,
Springer
Jukka SaTanen Department of Mathematical Sciences University of OuIu 90014 OuIu, Finland e-mail: [email protected] Gennadi Vainikko Institute of Mathematics Helsinki University of Technology 02150 Espoo, Finland e-mail: [email protected]
Library of Congress Cataloging·in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnahme Saranen, Jukka: Periodic integral and pseudodifferential equations with numerical approximation / Jukka Saranen ; Gennadi Vainikko. Berlin ; Heidelberg ; New York; Barcelona; Hong Kong ; London ; Milan; Paris; Tokyo : Springer, 2002 (Springer monographs in mathematics)
Mathematics Subject Classification (2000): 31A10, 35J05, 35J25, 41A15, 42A15, 45A05, 45E05, 46E35, 47A53, 47G30, 65N38, 65R20 ISSN 1439-7382 ISBN 978-3-642-07538-4 ISBN 978-3-662-04796-5 (eBook) DOI 10.1007/978-3-662-04796-5 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specificaIly the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, '965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under the German Copyright Law. http://www.springer.de
e Springer-Verlag Berlin Heidelberg 2002 Originally published 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 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. SPIN: 10795403
46/3142LK - 5 4 3 21 0 - Printed on acid-free paper
Preface
This is a self-contained course book for graduate/postgradute students and it can be considered also as a scientific monograph. The purpose of the book is introduce the reader to the modern treatment of boundary value problems and integral equations. We do this by using the theory of pseudodifferential operators. The theory of pseudodifferential operators in ]Rn origins from the works of Kohn and Nirenberg, Hörmander '65, and others. In this monograph we cover the theory of periodie pseudodifferential equations, or pseudodifferential equations on the unit circle introduced by Agranovieh '79. During the last twenty years periodie pseudodifferential operators occurred to be also a powerful tool in numerieal analysis. The content of the book includes the following items. We begin with the Fredholm operators and Krylov subspace methods such as GMRES and conjugate gradien
