Numerical Integration of the Nose-Hoover-Langevin Equations

2 Numerical Integration of the Nose-Hoover-Langevin Equations 

Many older schemes for Nos6-Hoover and Langevin dynamics make use of computational shortcuts to (for example) reduce the number of computed random values per iteration, reduce the data storage needed for an algorithm or replace functions that are costly to evaluate (e.g. exponential or trigonometric functions) 

We can apply the splitting approach considered in Chap. 7 to integrate equations (8.27H8.29). One suitable choice of algorithm that we shall use in the following subsection is 

This numerical method requires only one evaluation of the force per timestep. It also reduces to a Nos6-Hoover integrator when y = 0, and as it solves the Ornstein-Uhlenbeck process exactly, it is stable under the large (or infinite) limit of friction. 

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