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# Accession Number:

## AD0735403

# Title:

## Stability of Difference Approximations to Differential Equations

# Descriptive Note:

# Corporate Author:

## BROWN UNIV PROVIDENCE RI DIV OF APPLIED MATHEMATICS

# 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.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#