  The Generalized Langevin Equation (GLE) has been recently suggested to
simulate the time evolution of classical solid and molecular systems when
considering general non-equilibrium processes. In this approach, a part of the
whole system (an open system), which interacts and exchanges energy with its
dissipative environment, is studied. Because the GLE is derived by projecting
out exactly the harmonic environment, the coupling to it is realistic, while
the equations of motion are non-Markovian. Although the GLE formalism has
already found promising applications, e.g., in nanotribology and as a powerful
thermostat for equilibration in classical molecular dynamics simulations,
efficient algorithms to solve the GLE for realistic memory kernels are highly
non-trivial, especially if the memory kernels decay non-exponentially. This is
due to the fact that one has to generate a colored noise and take account of
the memory effects in a consistent manner. In this contribution, we present a
simple, yet efficient, algorithm for solving the GLE for practical memory
kernels and we demonstrate its capability for the exactly solvable case of a
harmonic oscillator coupled to a Debye bath.
