On the Existence and the Applications of Modified Equations for Stochastic Differential Equations
SIAM Journal on Scientific Computing
A patch that imparts unconditional stability to explicit integrators for Langevin-like equations
Journal of Computational Physics
Variational integrators for electric circuits
Journal of Computational Physics
Variational integrators for the dynamics of thermo-elastic solids with finite speed thermal waves
Journal of Computational Physics
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This paper presents a Lie-Trotter splitting for inertial Langevin equations (geometric Langevin algorithm) and analyzes its long-time statistical properties. The splitting is defined as a composition of a variational integrator with an Ornstein-Uhlenbeck flow. Assuming that the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial Langevin equations to within the accuracy of the variational integrator in representing the Hamiltonian. In particular, if the variational integrator admits no energy error, then the method samples the invariant measure of inertial Langevin equations without error. Numerical validation is provided using explicit variational integrators with first-, second-, and fourth-order accuracy.