Numerical Methods for Engineers

Numerical Methods for EngineersSEVENTH EDITIONS teven C. ChapraBerger Chair in Computing and EngineeringTufts UniversityRaymond P. CanaleProfessor Emeritus of Civil EngineeringUniversity of MichiganNUMERICAL Methods FOR Engineers , SEVENTH EDITIONP ublished by McGraw-Hill Education, 2 Penn Plaza, New York, NY 10121. Copyright 2015 by McGraw-Hill Education. All rights reserved. Printed in the United States of America. Previous editions 2010, 2006, and 2002. No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance ancillaries, including electronic and print components, may not be available to customers outside the United book is printed on acid-free paper.

29.2 Solution Technique 854 29.3 Boundary Conditions 860 29.4 The Control-Volume Approach 866 29.5 Software to Solve Elliptic Equations 869 Problems 870 CHAPTER 30 Finite Difference: Parabolic Equations 873 30.1 The Heat-Conduction Equation 873 30.2 Explicit Methods 874 30.3 A Simple Implicit Method 878 30.4 The Crank-Nicolson Method 882

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