Abstract
We compare two numerical algorithms for the computer modeling of the thermal decay process (Kramers problem) solving the stochastic (Langevin) equations for the generalized coordinate and its conjugate momentum. These are known in the literature (i) the ALGO algorithm including in the fluctuation part the terms up to τ3/2 (t is the time step of the numerical modeling) and (ii) the Euler-Maruyama algorithm including in the fluctuation part only the terms proportional to τ1/2. We concentrate on the quasistationary decay rate and transient time. The ALGO algorithm appears to be more efficient, however, the optimal size of the time step has a strong and non-trivial dependence upon the dissipation strength and governing parameter.
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