Accession Number:
AD0735403
Title:
Stability of Difference Approximations to Differential Equations
Descriptive Note:
Corporate Author:
BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS
Personal Author(s):
Report Date:
1972-01-01
Pagination or Media Count:
16.0
Abstract:
Consider the diferential equation 1 x dor fx in a Banach space and let x be an equilibrium. The basic question treated is the following if x is asymptotically stable and if 2 x subK 1 x sub K h phi x sub k, h is a one-step method, with fixed step size h, for integrating 1, then does the sequence x sub K converge to x. It is shown that uniform asymptotic stability of 1 implies stability of 2 and that exponential asymptotic stability of 1 implies asymptotic stability of 2.
Descriptors:
Subject Categories:
- Theoretical Mathematics