  We study a novel class of numerical integrators, the adapted nested
force-gradient schemes, used within the molecular dynamics step of the Hybrid
Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on
the lattice, a well known benchmark problem. We derive the analytical basis of
nested force-gradient type methods and demonstrate the advantage of the
proposed approach, namely reduced computational costs compared with other
numerical integration schemes in HMC.
