Stability of a saddle node bifurcation under numerical approximations

Authors:
Ming-Chia Li
Affiliations:
-
Venue:
Computers & Mathematics with Applications
Year:
2005

Citing 3
Cited 0

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods

The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods
Structural stability of Morse-Smale gradient-like flows under discretizations

SIAM Journal on Mathematical Analysis
Structural stability for the Euler method

SIAM Journal on Mathematical Analysis

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Abstract

In this paper, we show that the solution flows generated by a one-parameter family of ordinary differential equations are stable under their numerical approximations in a vicinity of a saddle node. Our result sharpens the one in [^1] and the proof is adapted from the method of Sotomayor in [^2^,^3].