Abstract
Thus, convergent methods generate numerical solutions that are arbitrarily close to the exact solution of the IVP provided that h is taken to be sufficiently small. Since non-convergent methods are of little practical use we shall henceforth assume that all LMMs used are convergent—they are consistent and zero-stable.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
E. Hairer and G. Wanner. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems. Springer-Verlag, Berlin, 2nd edition, 1996.
E. I. Jury. Theory and Application of thez-Transform Method. John Wiley and Sons, 1964.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2010 Springer-Verlag London Limited
About this chapter
Cite this chapter
Griffiths, D.F., Higham, D.J. (2010). Linear Multistep Methods—III: Absolute Stability. In: Numerical Methods for Ordinary Differential Equations. Springer Undergraduate Mathematics Series. Springer, London. https://doi.org/10.1007/978-0-85729-148-6_6
Download citation
DOI: https://doi.org/10.1007/978-0-85729-148-6_6
Published:
Publisher Name: Springer, London
Print ISBN: 978-0-85729-147-9
Online ISBN: 978-0-85729-148-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)