Chapter 4. Linear Multistep Methods

  1. J. C. Butcher

Published Online: 18 MAR 2008

DOI: 10.1002/9780470753767.ch4

Numerical Methods for Ordinary Differential Equations, Second Edition

Numerical Methods for Ordinary Differential Equations, Second Edition

How to Cite

Butcher, J. C. (2008) Linear Multistep Methods, in Numerical Methods for Ordinary Differential Equations, Second Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470753767.ch4

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:

  • linear multistep methods;
  • third order Adams–Bashforth method;
  • convergent linear multistep;
  • ‘backward difference formulae’ or BDF;
  • error growth;
  • Newton–Cotes formulae;
  • G stability;
  • PEC and PECE methods;
  • effective order concept

Summary

This chapter contains sections titled:

  • Preliminaries

  • The Order of Linear Multistep Methods

  • Errors and Error Growth

  • Stability Characteristics

  • Order and Stability Barriers

  • One-Leg Methods and G-stability

  • Implementation Issues