Computer simulation of liquids
Computer simulation of liquids
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Backward Error Analysis for Numerical Integrators
SIAM Journal on Numerical Analysis
Understanding Molecular Simulation: From Algorithms to Applications
Understanding Molecular Simulation: From Algorithms to Applications
Monitoring energy drift with shadow Hamiltonians
Journal of Computational Physics
On the estimation and correction of discretization error in molecular dynamics averages
Applied Numerical Mathematics
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We present the results of a set of numerical experiments designed to investigate the appropriateness of various integration schemes for molecular dynamics simulations. In particular, we wish to identify which numerical methods, when applied to an ergodic Hamiltonian system, sample the state-space in an unbiased manner. We do this by describing two Hamiltonian system for which we can analytically compute some of the important statistical features of its trajectories, and then applying various numerical integration schemes to them. We can then compare the results from the numerical simulation against the exact results for the system and see how closely they agree. The statistic we study is the empirical distribution of particle velocity over long trajectories of the systems. We apply four methods: one symplectic method (Stormer-Verlet) and three energy-conserving step-and-project methods. The symplectic method performs better on both test problems, accurately computing empirical distributions for all step-lengths consistent with stability. Depending on the test system and the method, the step-and-project methods are either no longer ergodic for any step length (thus giving the wrong empirical distribution) or give the correct distribution only in the limit of step-size going to zero.