  This study explores the potential of modern implicit solvers for stochastic
partial differential equations in the simulation of real-time complex Langevin
dynamics. Not only do these methods offer asymptotic stability, rendering the
issue of runaway solution moot, but they also allow us to simulate at
comparatively largeLangevin time steps, leading to lower computational cost. We
compare different ways of regularizing the underlying path integral and
estimate the errors introduced due to the finite Langevin time. Based on that
insight, we implement benchmark (non-)thermal simulations of the quantum
anharmonic oscillator on the canonical Schwinger-Keldysh contour of short
real-time extent.
