Accession Number:

ADA029731

Title:

On Liapunov Stability of Stiff Non-Linear Multistep Difference Equations,

Descriptive Note:

Corporate Author:

IBM THOMAS J WATSON RESEARCH CENTER YORKTOWN HEIGHTS N Y

Personal Author(s):

Report Date:

1976-03-11

Pagination or Media Count:

40.0

Abstract:

The concepts of G-stability and G,mu-stability recently introduced by Dahlquist are useful for discussing Liapunov stability of solutions to systems of non-linear difference equations, generated by applying linear multistep formulas to monotone, dissipative, arbitrarily stiff systems of non-linear differential equations. In this paper, the theory of G-stability and G,mu-stability is reviewed and a construction is proposed which facilitates the finding of a quadratic Liapunov function. By this construction it is proved that, for the four-parameter family of all three-step formulas which are second-order accurate, A-stability is necessary and sufficient for G-stability. Some results on G,mu-stability are also obtained by this construction.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE