Elements of Scientific Computing
Science used to be experiments and theory, now it is experiments, theory and computations. The computational approach to understanding nature and technology is currently flowering in many fields such as physics, geophysics, astrophysics, chemistry, biolog
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Editors Timothy J. Barth Michael Griebel David E. Keyes Risto M. Nieminen Dirk Roose Tamar Schlick
For further volumes: http://www.springer.com/series/5151
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Aslak Tveito • Hans Petter Langtangen Bjørn Frederik Nielsen • Xing Cai
Elements of Scientific Computing With 88 Figures and 18 Tables
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Aslak Tveito Hans Petter Langtangen Xing Cai Center for Biomedical Computing Simula Research Laboratory P.O. Box 134 1325 Lysaker Norway [email protected] [email protected] [email protected] and Department of Informatics University of Oslo P.O. Box 1080 Blindern 0316 Oslo Norway
Bjørn Frederik Nielsen Department of Mathematical Sciences and Technology Norwegian University of Life Sciences P.O. Box 5003 1432 Ås Norway [email protected] and Center for Biomedical Computing Simula Research Laboratory P.O. Box 134 1325 Lysaker Norway
Aslak Tveito has received financial support from the Norwegian Non-fiction Literature Fund.
ISSN 1611-0994 ISBN 978-3-642-11298-0 e-ISBN 978-3-642-11299-7 DOI 10.1007/978-3-642-11299-7 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2010936979 Mathematics Subject Classification (2010): 97-01, 97M10, 97N80 © Springer-Verlag Berlin Heidelberg 2010 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, 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, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. 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. Cover design: deblik, Berlin Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Science used to be experiments and theory; now it is experiments, theory, and computations. The computational approach to understanding nature and technology is currently expanding in many fields, such as physics, mechanics, geophysics, astrophysics, chemistry, biology, and most engineering disciplines. The computational methods used in these branches are very similar, and this book is a first introduction to such methods. Many books have been written on the subject. The present text aims to provide a gentle introduction, explaining the methods through examples taken from various fields of science. As a computational scientist, you will work with other applications, models, and methods than those covered herein. The field is vast and it is impossible to capture more than a small fraction of it in a reasonably sized text. Therefore, we will t
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