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Related Experiment Videos

Shadowing breakdown and large errors in dynamical simulations of physical systems.

Timothy D Sauer1

  • 1Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 23, 2002
PubMed
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Tiny noise can cause huge errors in long physical simulations. A new scaling law reveals how discretization and truncation errors amplify small inputs, impacting simulation statistics and challenging trajectory averages.

Area of Science:

  • Computational physics
  • Numerical analysis

Background:

  • Simulations are vital for studying physical systems.
  • Discretization and truncation errors pose challenges for long dynamical simulations.

Purpose of the Study:

  • To describe a general mechanism causing large errors from small noise inputs in simulations.
  • To provide a scaling law for these errors.

Main Methods:

  • Theoretical analysis of simulation error propagation.
  • Development of a scaling law relating error size to noise level and system dynamics.

Main Results:

  • A mechanism is identified where small noise inputs lead to errors several orders of magnitude larger.
  • A scaling law is derived for quantifying these simulation errors.

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Conclusions:

  • The findings question the reliability of trajectory averages for systems with specific dynamics, like fluctuating Lyapunov exponents.
  • Highlights the critical impact of numerical errors on simulation outcomes in computational physics.