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Authors: David F. Griffiths and Desmond J. Higham Springer Undergraduate Mathematics Series Contents 1. ODEs-An Introduction 2. Euler's Method 3. The Taylor Series Method 4. Linear Multistep Methods-I 5. Linear Multistep Methods-II 6. Linear Multistep Methods-III 7. Linear Multistep Methods-IV 8. Linear Multistep Methods-V 9. Runge-Kutta Mehtod-I:Order Conditions 10. Runge-Kutta Mehtod-II: Absolute Stability 11. Adaptive Step Size Selection 12. Long-term Dynamics 13. Modified Equations 14. Geometric Integration Part I-Invariants 15. Geometric Integration Part II- Hamiltonian Dynamics 16. Stochastic Differential Equations
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Springer Undergraduate Mathematics Series
Advisory Board
M.A.J. Chaplain University of Dundee
K. Erdmann University of Oxford
A. MacIntyre Queen Mary, University of London
E. S
¨
uli University of Oxford
For other titles published in this series, go to
www.springer.com/series/3423
M.R. Tehranchi University of Cambridge
J.F. Toland University of Bath
David F. Griffiths · Desmond J. Higham
Numerical Methods for
Ordinary Differential
Equations
Initial Value Problems
123
David F. Griffiths
Mathematics Division
University of Dundee
Dundee
dfg@maths.dundee.ac.uk
Desmond J. Higham
Department of Mathematics and Statistics
University of Strathclyde
Glasgow
djh@maths.strath.ac.uk
Springer Undergraduate Mathematics Series ISSN 1615-2085
ISBN 978-0-85729-147-9 e-ISBN 978-0-85729-148-6
DOI 10.1007/978-0-85729-148-6
Springer London Dordrecht Heidelberg New York
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
Library of Congress Control Number: 2010937859
Mathematics Subject Classification (2010): 65L05, 65L20, 65L06, 65L04, 65L07
c
Springer-Verlag London Limited 2010
Apart from any fair dealing for the purposes of research or private study, or criticism or review, as
permitted under the Copyright, Designs and Patents Act 1988, this publication may only be reproduced,
stored or transmitted, in any form or by any means, with the prior permission in writing of the
publishers, or in the case of reprographic reproduction in accordance with the terms of licenses issued
by the Copyright Licensing Agency. Enquiries concerning reproduction outside those terms should be
sent to the publishers.
The use of 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 laws and regulations and therefore free
for general use.
The publisher makes no representation, express or implied, with regard to the accuracy of the information
contained in this book and cannot accept any legal responsibility or liability for any errors or omissions
that may be made.
Printed on acid-free paper
Springer is part of Springer Science+Business Media (www.springer.com)
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