Journal ArticleDOI
Analysis of a few numerical integration methods for the Langevin equation
Wei Wang,Robert D. Skeel +1 more
Reads0
Chats0
TLDR
In this paper, the position recurrence relation of several existing numerical integrators for the Langevin equation and use the modified equation approach to analyse their accuracy was studied. But their analysis was restricted to a restricted class of velocity definitions, those that lead to explicit starting procedures.Abstract:
We study the position recurrence relation of several existing numerical integrators for the Langevin equation and use the modified equation approach to analyse their accuracy. We show that for the harmonic oscillator, the BBK integrator converges weakly with order 1 while the vGB82 and Langevin impulse (LI)‡ integrator converge weakly with order 2. We also study a restricted class of velocity definitions—those that lead to explicit starting procedures. We show that some recurrence relations exact for constant force, can achieve the exact virial relation by a proper definition of velocity, extending the result of Pastor et al. on the analysis of BBK integrators in 1988.read more
Citations
More filters
Journal ArticleDOI
Scalable molecular dynamics with NAMD
James C. Phillips,Rosemary Braun,Wei Wang,James C. Gumbart,Emad Tajkhorshid,Elizabeth Villa,Christophe Chipot,Robert D. Skeel,Laxmikant V. Kale,Klaus Schulten +9 more
TL;DR: NAMD as discussed by the authors is a parallel molecular dynamics code designed for high-performance simulation of large biomolecular systems that scales to hundreds of processors on high-end parallel platforms, as well as tens of processors in low-cost commodity clusters, and also runs on individual desktop and laptop computers.
Journal ArticleDOI
Second-order integrators for Langevin equations with holonomic constraints
TL;DR: This work indicates how to generalize this scheme for the integration of the Langevin equation to situations where holonomic constraints are added and shows that the resulting scheme remains second-order accurate.
Journal ArticleDOI
A simple and effective Verlet-type algorithm for simulating Langevin dynamics
TL;DR: In this article, the Stormer-Verlet algorithm for simulating second order differential equations with linear friction with associated stochastic noise is presented, and analytically demonstrated that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential.
Journal ArticleDOI
A simple and effective Verlet-type algorithm for simulating Langevin dynamics
TL;DR: The revision addresses the inclusion of linear friction with associated stochastic noise, and it is demonstrated that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential.
References
More filters
Book
Computer Simulation of Liquids
Michael P. Allen,D. J. Tildesley +1 more
TL;DR: In this paper, the gear predictor -corrector is used to calculate forces and torques in a non-equilibrium molecular dynamics simulation using Monte Carlo methods. But it is not suitable for the gear prediction problem.
Book
Numerical Solution of Stochastic Differential Equations
Peter E. Kloeden,Eckhard Platen +1 more
TL;DR: In this article, a time-discrete approximation of deterministic Differential Equations is proposed for the stochastic calculus, based on Strong Taylor Expansions and Strong Taylor Approximations.
Journal ArticleDOI
An analysis of the accuracy of Langevin and molecular dynamics algorithms
TL;DR: In this paper, the mean squared positions and velocities of a harmonic oscillator are derived for Langevin dynamics algorithms valid in the high and low friction limits, and for the Verlet algorithm.
Journal ArticleDOI
Stochastic boundary conditions for molecular dynamics simulations of ST2 water
TL;DR: The deformable stochastic boundary method developed previously for treating simple liquids without periodic boundary conditions, is extended to the ST2 model of water in this article, which is illustrated by a molecular dynamics simulation of a sphere containing 98 water molecules.