How Long Do Numerical Chaotic Solutions Remain Valid?
- 7 July 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 79 (1) , 59-62
- https://doi.org/10.1103/physrevlett.79.59
Abstract
Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of “how good” and “for how long” the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities that are easily computable in practice. The scaling theory is verified against a physical model.Keywords
This publication has 10 references indexed in Scilit:
- Numerical Shadowing Near Hyperbolic TrajectoriesSIAM Journal on Scientific Computing, 1995
- Obstructions to Shadowing When a Lyapunov Exponent Fluctuates about ZeroPhysical Review Letters, 1994
- Shadows, chaos, and saddlesApplied Numerical Mathematics, 1993
- On the reliability of gravitational N-body integrationsMonthly Notices of the Royal Astronomical Society, 1992
- On the numerical computation of orbits of dynamical systems: The one-dimensional caseJournal of Dynamics and Differential Equations, 1991
- Shadowing of physical trajectories in chaotic dynamics: Containment and refinementPhysical Review Letters, 1990
- Numerical orbits of chaotic processes represent true orbitsBulletin of the American Mathematical Society, 1988
- Do numerical orbits of chaotic dynamical processes represent true orbits?Journal of Complexity, 1987
- ω-Limit sets for Axiom A diffeomorphismsJournal of Differential Equations, 1975
- Nongenericity of Ω-stabilityPublished by American Mathematical Society (AMS) ,1970