Job Name: Cyan = PM/3S5 3605085t In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t INTRODUCTION TO COMPUTATIONAL SCIENCE Second Edition In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t INTRODUCTION TO COMPUTATIONAL SCIENCE MODELING AND SIMULATION FOR THE SCIENCES Second Edition Angela B. Shiflet and George W. Shiflet PRINCETON UNIVERSITY PRESS PRINCETON AND OXFORD In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t Copyright © 2014 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW press.princeton.edu Cover art by Linda Stoudt, Untitled 2005 (detail), 4 3/16 × 3, oil on paper All Rights Reserved Library of Congress Cataloging-in-Publication Data Shiflet, Angela B. Introduction to computational science : modeling and simulation for the sciences / Angela B. Shiflet and George W. Shiflet. — Second edition. pages cm Includes bibliographical references and index. ISBN 978-0-691-16071-9 (hardcover : alk. paper) 1. Computer sci- ence. 2. Computer simulation. 3. Mathematical models. 4. Computational complexity. I. Shiflet, George W. II. Title. QA76.6.S54143 2014 004—dc23 2013024877 The epigraph in module 7.15 is © Woody Allen British Library Cataloging-in-Publication Data is available This book has been composed in Times Roman Printed on acid-free paper. ∞ Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t Dedicated to Robert K. Cralle, Theodore H. Einwohner, and George A. Michael Lawrence Livermore Laboratory and Robert M. Panoff The Shodor Education Foundation, whose friendship and guidance we have treasured In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option. Job Name: Cyan = PM/3S5 3605085t CONTENTS Preface xxiii 1 O VERVIEW Module 1.1 Overview of Computational Science 3 Projects 6 References 6 Module 1.2 The Modeling Process 7 Introduction 7 Model Classifications 8 Steps of the Modeling Process 9 Exercises 11 References 12 2 S YSTEM DYNAMICS PROBLEMS WITH RATE PROPORTIONAL TO AMOUNT Module 2.1 System Dynamics Tool—Tutorial 1 15 Download 15 Introduction 15 Module 2.2 Unconstrained Growth and Decay 17 Introduction 17 Rate of Change 17 Differential Equation 19 Difference Equation 20 Simulation Program 24 Analytical Solution: Introduction 25 Analytical Solution: Explanation with Indefinite Integrals (Optional) 26 Analytical Solution: Explanation with Derivatives (Optional) 26 Completion of the Analytical Solution 27 Further Refinement 28 Unconstrained Decay 28 Reports for System Dynamics Models 30 Exercises 31 Projects 32 Answers to Quick Review Questions 33 Reference 33 Module 2.3 Constrained Growth 34 Introduction 34 Carrying Capacity 35 Revised Model 36 Equilibrium and Stability 39 In order to view this proof accurately, the Overprint Preview Option must be checked in Acrobat Professional or Adobe Reader. Please contact your Customer Service Rep- resentative if you have questions about finding the option.