Spectral Methods in Chemistry and Physics Applications to Kinetic Th
This book is a pedagogical presentation of the application of spectral and pseudospectral methods to kinetic theory and quantum mechanics. There are additional applications to astrophysics, engineering, biology and many other fields. The main objective of
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Bernard Shizgal
Spectral Methods in Chemistry and Physics Applications to Kinetic Theory and Quantum Mechanics
Spectral Methods in Chemistry and Physics
Scientific Computation Editorial Board J.-J. Chattot, Davis, CA, USA P. Colella, Berkeley, CA, USA R. Glowinski, Houston, TX, USA M.Y. Hussaini, Tallahassee, FL, USA P. Joly, Le Chesnay, France D.I. Meiron, Pasadena, CA, USA O. Pironneau, Paris, France A. Quarteroni, Lausanne, Switzerland and Politecnico of Milan, Milan, Italy J. Rappaz, Lausanne, Switzerland B. Rosner, Chicago, IL, USA P. Sagaut, Paris, France J.H. Seinfeld, Pasadena, CA, USA A. Szepessy, Stockholm, Sweden M.F. Wheeler, Austin, TX, USA
More information about this series at http://www.springer.com/series/718
Bernard Shizgal
Spectral Methods in Chemistry and Physics Applications to Kinetic Theory and Quantum Mechanics
123
Bernard Shizgal University of British Columbia Vancouver, BC Canada
ISSN 1434-8322 Scientific Computation ISBN 978-94-017-9453-4 DOI 10.1007/978-94-017-9454-1
ISBN 978-94-017-9454-1
(eBook)
Library of Congress Control Number: 2014955993 Springer Dordrecht Heidelberg New York London © Springer Science+Business Media Dordrecht 2015 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. Printed on acid-free paper Springer Science+Business Media B.V. Dordrecht is part of Springer Science+Business Media (www.springer.com)
Preface
Spectral and pseudospectral methods have become increasingly popular as higher order methods for the solution of partial differential and integral equations (Azaïez et al. 2013). A spectral method refers to the representation of the solution of some problem in a basis set of orthogonal functions, whereas a pseudospectral approach, sometimes referred to as a collocation, is based on the representation of the solution with the function values at a set of discrete points. For the smooth solutions of particular problems, these methods can provide exponential convergence of the solutions versus the number of basis
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