Stability of Difference Approximations to Differential Equations

Stability of Difference Approximations to Differential Equations

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), th...

Ausführliche Beschreibung

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Bibliographische Detailangaben
Hauptverfasser: Falb, Peter L, Groome, George M , Jr
Format: Report
Sprache:eng
Schlagworte:
APPROXIMATION(MATHEMATICS)
ASYMPTOTIC SERIES
ASYMPTOTIC STABILITY
BANACH SPACE
DIFFERENTIAL EQUATIONS
INTEGRATION
NUMERICAL ANALYSIS
NUMERICAL INTEGRATION
STABILITY
Theoretical Mathematics
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Zusammenfassung: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).