Fundamentals of Scientific Computing
The book of nature is written in the language of mathematics -- Galileo Galilei How is it possible to predict weather patterns for tomorrow, with access solely to today’s weather data? And how is it possible to predict the aerodynamic behavior
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Bertil Gustafsson
Fundamentals of Scientific Computing
Bertil Gustafsson Information Technology Uppsala University PO Box 337 751 05 Uppsala Sweden [email protected]
ISSN 1611-0994 ISBN 978-3-642-19494-8 e-ISBN 978-3-642-19495-5 DOI 10.1007/978-3-642-19495-5 Springer Heidelberg Dordrecht London New York Library of Congress Control Number: 2011929632 Mathematics Subject Classification (2000): 65-01 © Springer-Verlag Berlin Heidelberg 2011 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
Computers play an increasingly important role in our society. A breakdown of all computer systems would cause a breakdown of almost all activities of daily life. Furthermore, personal computers are available in almost every home in the industrialized world. But there is one sector where computers have a more strategic role, and that is in science and technology. A large number of physical and engineering problems are solved by the use of advanced computers. The first aircraft were designed by very clever individuals who understood the basic principles of aerodynamics, but today this is not enough. No manufacturer would start building a new aeroplane without extensive computer simulations of various models. Another example where computer simulation is a necessary tool is weather prediction. We know that these predictions are not completely accurate, but are still good enough to get a fairly good idea about the weather for the next few days. The question then is: how is it at all possible to predict the future of a physical system like the atmosphere around the globe? Or in the first example: how is it possible to predict the flight properties of an aircraft that has not yet been built, and where not even a model of the aircraft is available to put in a wind tunnel? No matter how powerful the computers are, we have to provide them with a program that tells them how to carry out the simulation. How is this program constructed? The fundamental basis for these algorithms is a mathematical model of some kind that provides certain relations between th
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