Accurate and robust splitting methods for the generalized Langevin equation with a positive Prony series memory kernel

Abstract

We study numerical methods for the generalized Langevin equation (GLE) with a positive Prony series memory kernel, in which case the GLE can be written in an extended variable Markovian formalism. We propose a new splitting method that is easy to implement and is able to substantially improve the accuracy and robustness of GLE simulations in a wide range of the parameters. An error analysis is performed in the case of a one-dimensional harmonic oscillator, revealing that several averages are exact for the newly proposed method. Various numerical experiments in both equilibrium and nonequilibrium simulations are also conducted to compare the method with popular alternatives in interacting multi-particle systems.

References in corpus (7)

• Nuclear quantum effects in solids using a colored-noise thermostat
• Colored-noise thermostats à la carte
• Data-driven molecular modeling with the generalized Langevin equation
• High-Order Langevin Diffusion Yields an Accelerated MCMC Algorithm
• Trotter Derivation of Algorithms for Brownian and Dissipative Particle Dynamics
• On the Generalised Langevin Equation for Simulated Annealing
• Accurate and efficient splitting methods for dissipative particle dynamics

Cited by in corpus (1)

• Stochastic Norton dynamics: An alternative approach for the computation of transport coefficients in dissipative particle dynamics