Stability of Difference Approximations to Differential Equations
Abstract
Consider the diferential equation (1) x dor = f(x) 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 sub(K + 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).
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1972
- Accession Number
- AD0735403
Entities
People
- George M. Groome Jr
- Peter L. Falb
Organizations
- Brown University