Mathematical Modelling Concepts and Case Studies
Over the past decade there has been an increasing demand for suitable material in the area of mathematical modelling as applied to science and engineering. There has been a constant movement in the emphasis from developing proficiency in purely mathematic
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MATHEMATICAL MODELLING: Theory and Applications VOLUME 6 This series is aimed at publishing work dealing with the definition, development and application of fundamental theory and methodology, computational and algorithmic implementations and comprehensive empirical studies in mathematical modelling. Work on new mathematics inspired by the construction of mathematical models, combining theory and experiment and furthering the understanding of the systems being modelled are particularly welcomed. Manuscripts to be considered for publication lie within the following, non-exhaustive list of areas: mathematical modelling in engineering, industrial mathematics, control theory, operations research, decision theory, economic modelling, mathematical programmering, mathematical system theory, geophysical sciences, climate modelling, environmental processes, mathematical modelling in psychology, political science, sociology and behavioural sciences, mathematical biology, mathematical ecology, image processing, computer vision, artificial intelligence, fuzzy systems, and approximate reasoning, genetic algorithms, neural networks, expert systems, pattern recognition, clustering, chaos and fractals. Original monographs, comprehensive surveys as well as edited collections will be considered for publication. Editors: R. Lowen (Antwerp, Belgium) Editorial Board: G.I. Klir (New York, U.S.A.) I.-L. Lions (Paris, France) P.G. Mezey (Saskatchewan, Canada) F. Pfeiffer (Munchen, Germany) H.-I. Zimmerman (Aachen, Germany)
The titles published in this series are listed at the end of this volume.
Mathematical Modelling Concepts and Case Studies
by J. Caldwell City University of Hong Kong, Kowloon, Hong Kong
and
Y. M. Ram Louisiana State University, Baton Rouge, U.S.A.
SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN 978-90-481-5263-6 ISBN 978-94-017-2201-8 (eBook) DOI 10.1007/978-94-017-2201-8
Printed on acid-free paper
AII Rights Reserved
© 1999 Springer Science+-Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1999 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner.
CONTENTS
Preface
IX
Part I Continuous and Discrete Modelling
1
Chapter 1 Formulation of Mathematical Models
3
1.1 1.2 1.3 1.4 1.5 1.6 1.7
The Mathematical Modelling Process Input-Output Principle Rate Models Models Involving Recurrence Relations Optimization Models Sensitivity Analysis Exercises
Chapter 2 Compartment Problems 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9
Introduction Model for Temperature Change in a Single Room Model for a Single Tank System Well-Posed Problems A Nonisothermal Holding Tank Multi-Compartment Problems Introduction of Organisms Models Involving Systems of Differential Equations Exercises
3 5 7 14
