Chapter 2. Numerical Differential Equation Methods

  1. J. C. Butcher

Published Online: 18 MAR 2008

DOI: 10.1002/9780470753767.ch2

Numerical Methods for Ordinary Differential Equations, Second Edition

Numerical Methods for Ordinary Differential Equations, Second Edition

How to Cite

Butcher, J. C. (2008) Numerical Differential Equation Methods, in Numerical Methods for Ordinary Differential Equations, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470753767.ch2

Author Information

  1. The University of Auckland, New Zealand

Publication History

  1. Published Online: 18 MAR 2008
  2. Published Print: 7 MAR 2008

ISBN Information

Print ISBN: 9780470723357

Online ISBN: 9780470753767

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Keywords:

  • stability region - Euler method;
  • numerical differential equation methods;
  • Lipschitz condition;
  • global truncation error;
  • Runge–Kutta method;
  • backward difference method;
  • ‘Adams–Moulton’ methods;
  • ‘modified multistep methods’

Summary

This chapter contains sections titled:

  • The Euler Method

  • Analysis of the Euler Method

  • Generalizations of the Euler Method

  • Runge–Kutta Methods

  • Linear Multistep Methods

  • Taylor Series Methods

  • Hybrid Methods

  • Introduction to Implementation