Numerical Methods for Ordinary Differential Equations

Initial Value Problems

  • David F. Griffiths
  • Desmond J. Higham

Part of the Springer Undergraduate Mathematics Series book series (SUMS)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. David F. Griffiths, Desmond J. Higham
    Pages 1-18
  3. David F. Griffiths, Desmond J. Higham
    Pages 19-31
  4. David F. Griffiths, Desmond J. Higham
    Pages 33-42
  5. David F. Griffiths, Desmond J. Higham
    Pages 43-60
  6. David F. Griffiths, Desmond J. Higham
    Pages 61-73
  7. David F. Griffiths, Desmond J. Higham
    Pages 75-94
  8. David F. Griffiths, Desmond J. Higham
    Pages 95-108
  9. David F. Griffiths, Desmond J. Higham
    Pages 109-121
  10. David F. Griffiths, Desmond J. Higham
    Pages 123-134
  11. David F. Griffiths, Desmond J. Higham
    Pages 135-143
  12. David F. Griffiths, Desmond J. Higham
    Pages 145-163
  13. David F. Griffiths, Desmond J. Higham
    Pages 165-176
  14. David F. Griffiths, Desmond J. Higham
    Pages 177-193
  15. David F. Griffiths, Desmond J. Higham
    Pages 195-206
  16. David F. Griffiths, Desmond J. Higham
    Pages 207-223
  17. David F. Griffiths, Desmond J. Higham
    Pages 225-241
  18. Back Matter
    Pages 243-271

About this book

Introduction

Numerical Methods for Ordinary Differential Equations is a self-contained introduction to a fundamental field of numerical analysis and scientific computation. Written for undergraduate students with a mathematical background, this book focuses on the analysis of numerical methods without losing sight of the practical nature of the subject.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge-Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

Keywords

Convergence Linear Multistep Mathematica Ordinary Differential Equations Runge-Kutta Stability calculus numerical analysis numerical methods ordinary differential equation

Authors and affiliations

  • David F. Griffiths
    • 1
  • Desmond J. Higham
    • 2
  1. 1., Mathematics DivisionUniversity of DundeeDundeeUnited Kingdom
  2. 2.Dept. MathematicsUniversity of StrathclydeGlasgowUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-85729-148-6
  • Copyright Information Springer-Verlag London Limited 2010
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-85729-147-9
  • Online ISBN 978-0-85729-148-6
  • Series Print ISSN 1615-2085
  • About this book