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):

• Falb, Peter L.
• Groome, George M., Jr

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:

• *DIFFERENTIAL EQUATIONS
• STABILITY
• NUMERICAL ANALYSIS
• INTEGRATION
• APPROXIMATION(MATHEMATICS)
• ASYMPTOTIC SERIES
• BANACH SPACE

Subject Categories:

• Theoretical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE