Analysis of a few numerical integration methods for the Langevin equation. Submitted for publication (2001) [2 citations — 1 self]
Abstract:
There are many numerical integration methods for the Langevin equation. In this thesis, we study the position recurrence relation of several existing numerical integration methods and use the modied equation approach to analyze their accuracy. We mainly consider three methods: one method rst proposed by Brunger et al in 1984, and generally referred to as the BBK method; one method proposed by van Gunsteren et al in 1982; and the Langevin impulse method, proposed by Skeel in 1999. We show that, for the harmonic oscillator, the BBK method converges weakly with order 1 while the other two method converge weakly with order 2. We also study a restricted class of velocity denitions | those that lead to explicit starting procedures. We consider the following two choices: (1) exact for constant force, (2) exact virial relation. We show that it is always possible to achieve an exact virial relation by a proper denition of velocity, extending the result of Pastor et al on the analysis of BBK methods in 1988. Furthermore, we use the modied equation approach to analyze the accuracy of a few numerical methods. iii
Citations
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