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Extrapolation and the Bulirsch-Stoer algorithm.

James L Monroe1

  • 1Department of Physics, Penn State University, Beaver Campus, 100 University Drive, Monaca, PA 15061-2799, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|August 22, 2002
PubMed
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The Bulirsch-Stoer algorithm improves statistical mechanics simulations by extrapolating finite systems to infinite ones. Using many smaller systems yields more accurate results than fewer larger ones.

Area of Science:

  • Statistical Mechanics
  • Computational Physics

Background:

  • The Bulirsch-Stoer algorithm is a numerical method used for extrapolation.
  • It has been applied in statistical mechanics to approximate infinite systems from finite ones since 1984.

Purpose of the Study:

  • To investigate the error characteristics of the Bulirsch-Stoer algorithm.
  • To determine how system size and number affect extrapolation accuracy in statistical mechanics.

Main Methods:

  • Applied the Bulirsch-Stoer algorithm to systems with known infinite behavior.
  • Analyzed the algorithm's error and performance based on input system parameters.

Main Results:

  • The study quantifies the error associated with the Bulirsch-Stoer extrapolation.

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  • Effectiveness is highly dependent on the number and size of input systems.
  • A greater number of smaller systems provides superior accuracy compared to fewer larger systems.

    • Conclusions:

    • The Bulirsch-Stoer algorithm is a valuable tool for finite-size scaling in statistical mechanics.
    • Optimizing the number and size of input systems is crucial for maximizing accuracy.
    • Employing numerous smaller systems is recommended for more reliable extrapolations.