2025/04/04 by Andrey Shkerin, Shkerin, Andrey, Sergey Sibiryakov +1 · 1 citation
Decision Sciences · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Cosmology and Nongalactic Astrophysics (astro-ph.CO) #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Probabilistic and Robust Engineering Design #Statistical Mechanics (cond-mat.stat-mech) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2504.03844
openalex publication_date 2025/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a method for constructing numerical schemes with up to 3rd strong convergence order for solution of a class of stochastic differential equations, including equations of the Langevin type. The construction proceeds in two stages. In the first stage one approximates the stochastic equation by a differential equation with smooth coefficients randomly sampled at each time step. In the second stage the resulting regular equation is solved with the conventional operator-splitting techniques. This separation renders the approach flexible, allowing one to freely combine the numerical techniques most suitable to the problem at hand. The approach applies to ordinary and partial stochastic differential equations. In the latter case, it naturally gives rise to pseudo-spectral algorithms. We numerically test the strong convergence of several schemes obtained with this method in mechanical examples. Application to partial differential equations is illustrated by real-time simulations of a scalar field with quartic self-interaction coupled to a heat bath. The simulations accurately reproduce the thermodynamic properties of the field and are used to explore dynamics of thermal false vacuum decay in the case of negative quartic coupling.