Adaptive numerical solution of Kadanoff-Baym equations

A time-stepping scheme with adaptivity in both the step size and integration order is presented context of non-equilibrium dynamics described via Kadanoff-Baym equations. The accuracy effectiveness algorithm are analysed by obtaining numerical solutions exactly solvable models. We find a significant reduction number time-steps compared to fixed-step methods. Due at least quadratic scaling equations, reducing amount steps can dramatically increase accessible time, opening door for study long-time interacting systems. selection illustrative examples provided, among them open quantum systems as well classical stochastic processes. An open-source implementation our scientific-computing language Julia made available.