Chapter 5. General Linear Methods

  1. J. C. Butcher

Published Online: 18 MAR 2008

DOI: 10.1002/9780470753767.ch5

Numerical Methods for Ordinary Differential Equations, Second Edition

Numerical Methods for Ordinary Differential Equations, Second Edition

How to Cite

Butcher, J. C. (2008) General Linear Methods, in Numerical Methods for Ordinary Differential Equations, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470753767.ch5

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:

  • general linear methods;
  • Runge–Kutta or linear multistep methods;
  • ‘generalized Pad′e approximations’;
  • A-stable methods;
  • local truncation error;
  • zero spectral radius;
  • IRKS parameter methods

Summary

This chapter contains sections titled:

  • Representing Methods in General Linear Form

  • Consistency, Stability and Convergence

  • The Stability of General Linear Methods

  • The Order of General Linear Methods

  • Methods with Runge–Kutta stability

  • Methods with Inherent Runge–Kutta Stability