Calculation of Lyapunov Exponents using Nonstandard Finite Difference Discretization Scheme: A Case Study

DOI10.1080/10236190310001625244zbMath1047.65109OpenAlexW1999798276MaRDI QIDQ4469973

Qiong Wu, Nariman Sepehri, Pooya Sekhavat

Publication date: 22 June 2004

Published in: Journal of Difference Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10236190310001625244

zbMATH Keywords

Lyapunov exponentsRunge-Kutta methodStabilityLyapunov direct methodNonsmooth dynamic systemsNonstandard finite difference schemeNumerical instabilitySwitching contact task control system

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Nonuniformly hyperbolic systems (Lyapunov exponents, Pesin theory, etc.) (37D25) Finite difference and finite volume methods for ordinary differential equations (65L12) Computational methods for ergodic theory (approximation of invariant measures, computation of Lyapunov exponents, entropy, etc.) (37M25) Numerical nonlinear stabilities in dynamical systems (65P40)

Related Items (4)

On stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping-a case study ⋮ On the use of nonstandard finite difference methods† ⋮ Switching contact task control in hydraulic actuators: Stability analysis and experimental evaluation ⋮ On stability analysis via Lyapunov exponents calculated based on radial basis function networks

Cites Work

• Calculation of Lyapunov exponents for dynamic systems with discontinuities.
• Discretizations of nonlinear differential equations using explicit finite order methods
• Suppression of numerically induced chaos with nonstandard finite difference schemes
• NUMERICAL STUDY OF A NON-STANDARD FINITE-DIFFERENCE SCHEME FOR THE VAN DER POL EQUATION

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