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

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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.
Original languageEnglish
Article number111332
JournalJournal of Computational Physics
Volume464
Early online date25 May 2022
DOIs
Publication statusPublished - 1 Sept 2022

Bibliographical note

Publisher Copyright:
© 2022 The Author(s)

Keywords

  • Error analysis
  • Generalized Langevin equation
  • Harmonic oscillator
  • Memory kernel
  • Splitting methods
  • Stochastic differential equations

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