Analysis of the backward‐euler/langevin method for molecular dynamics

Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


This paper develops the theory of a recently introduced computational method for molecular dynamics. The method in question uses the backward‐Euler method to solve the classical Langevin equations of a molecular system. Parameters are chosen to produce a cutoff frequency ωc, which may be set equal to kT/h to simulate quantum‐mechanical effects. In the present paper, an ensemble of identical Hamiltonian systems modeled by the backward‐Euler/Langevin method is considered, an integral equation for the equilibrium phase‐space density is derived, and an asymptotic analysis of that integral equation in the limit Δt → 0 is performed. The result of this asymptotic analysis is a second‐order partial differential equation for the equilibrium phase‐space density expressed as a function of the constants of the motion. This equation is solved in two special cases: a system of coupled harmonic oscillators and a diatomic molecule with a stiff bond.

Original languageEnglish (US)
Pages (from-to)599-645
Number of pages47
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - Jul 1990

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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