On the stability of numerical methods of Hopf points using backward error analysis

DOI10.1007/BF02238099zbMath0832.65088MaRDI QIDQ1895656

George W. Reddien

Publication date: 11 March 1996

Published in: Computing (Search for Journal in Brave)

zbMATH Keywords

stabilityHopf bifurcationRunge-Kutta methodPoincaré mapbackward error analysisadaptive mesh selectionAdams methodweakly attracting periodic solutions

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (2)

Discretizing the fold bifurcation - a conjugacy result ⋮ A method for the numerical computation of Hopf bifurcation

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• Runge–Kutta Methods for Dissipative and Gradient Dynamical Systems
• Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
• A Hopf bifurcation theorem for difference equations approximating a differential equation

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