Equivalence of operator-splitting schemes for the integration of the Langevin equation

Details Equivalence of operator-splitting schemes for the integration of the Langevin equation Equivalence of operator-splitting schemes for the integration of the Langevin equation

2006-07-24

arxiv.org/abs/cond-mat/0607596v1

Journal of Statistical Mechanics (2006) P08021

Physics

Condensed Matter

Statistical Mechanics

4 pages

Scientific paper

10.1088/1742-5468/2006/08/P08021

We investigate the equivalence of different operator-splitting schemes for the integration of the Langevin equation. We consider a specific problem, so called the directed percolation process, which can be extended to a wider class of problems. We first give a compact mathematical description of the operator-splitting method and introduce two typical splitting schemes that will be useful in numerical studies. We show that the two schemes are essentially equivalent through the map that turns out to be an automorphism. An associated equivalent class of operator-splitting integrations is also defined by generalizing the specified equivalence.

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