Defect-controlled numerical methods and shadowing for chaotic differential equations

DOI10.1016/0167-2789(92)90249-MzbMath0779.34035MaRDI QIDQ687822

Robert M. Corless

Publication date: 16 January 1994

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

shadowingchaotic differential equationsdefect-controlled numerical methodsvariable step-size codes

Mathematics Subject Classification ID

Error bounds for numerical methods for ordinary differential equations (65L70) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Dynamical systems and ergodic theory (37-XX) Numerical analysis in abstract spaces (65J99)

Related Items

What good are numerical simulations of chaotic dynamical systems? ⋮ On the nonlinear stability of the 1:1:1 ABC flow ⋮ Shifts of finite type as fundamental objects in the theory of shadowing ⋮ Shadowing, internal chain transitivity and \(\alpha \)-limit sets ⋮ On the susceptibility of numerical methods to computational chaos and superstability ⋮ Expansivity and unique shadowing ⋮ A survey of shadowing methods for numerical solutions of ordinary differential equations ⋮ Can a polynomial interpolation improve on the Kaplan-Yorke dimension? ⋮ Chaos control in the cerium-catalyzed Belousov-Zhabotinsky reaction using recurrence quantification analysis measures ⋮ Spectral element methods for nonlinear temporal dynamical systems ⋮ Preservation of shadowing in discrete dynamical systems ⋮ On inverse shadowing ⋮ When is the beginning the end? On full trajectories, limit sets and internal chain transitivity ⋮ Shadowing for induced maps of hyperspaces ⋮ Nonlinear stiffness, Lyapunov exponents, and attractor dimension

Uses Software

• Maple

Cites Work

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