  We propose a second order, fully semi-Lagrangian method for the numerical
solution of systems of advection-diffusion-reaction equations, which employs a
semi-Lagrangian approach to approximate in time both the advective and the
diffusive terms. Standard interpolation procedures are used for the space
discretization on structured and unstructured meshes. The proposed method
allows for large time steps, while avoiding the solution of large linear
systems, which would be required by an implicit time discretization technique.
Numerical experiments demonstrate the effectiveness of the proposed approach
and its superior efficiency with respect to more conventional explicit and
implicit time discretizations
