Chapter 3. Runge–Kutta Methods

  1. J. C. Butcher

Published Online: 18 MAR 2008

DOI: 10.1002/9780470753767.ch3

Numerical Methods for Ordinary Differential Equations, Second Edition

Numerical Methods for Ordinary Differential Equations, Second Edition

How to Cite

Butcher, J. C. (2008) Runge–Kutta Methods, in Numerical Methods for Ordinary Differential Equations, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470753767.ch3

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:

  • Runge–Kutta methods;
  • rooted tree and non-rooted trees;
  • ‘summation convention’;
  • Taylor series of exact solution;
  • pohutukawa (Metrosideros excelsa) or ‘New Zealand Christmas tree’;
  • ‘Radau I quadrature formula’

Summary

This chapter contains sections titled:

  • Preliminaries

  • Order Conditions

  • Low Order Explicit Methods

  • Runge–Kutta Methods with Error Estimates

  • Implicit Runge–Kutta Methods

  • Stability of Implicit Runge–Kutta Methods

  • Implementable Implicit Runge–Kutta Methods

  • Symplectic Runge–Kutta Methods

  • Algebraic Properties of Runge–Kutta Methods

  • Implementation Issues